We consider refinement of finite element discretizations by splitting nodes along edges. For

this process, we derive asymptotic expansions of Galerkin solutions of linear second-order

elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for

functionals such as the total potential energy, minimization of which decreases the approxi-

mation error in the energy norm. Hence, these sensitivities can be used to define indicators for

local h-refinement. Our results suggest that this procedure leads to an efficient adaptive re-

finement method. This presentation is concerned with a model problem in 1d. The extension

of this concept to higher dimensions will be the subject of forthcoming publications.

},
author = {Friederich, Jan and Leugering, Günter and Steinmann, Paul},
doi = {10.1002/gamm.201210012},
faupublication = {yes},
journal = {GAMM-Mitteilungen},
note = {UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anadap},
pages = {175-190},
peerreviewed = {unknown},
title = {{An} adaptive finite element method based on sensitivities for node insertion},
url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full},
volume = {35},
year = {2012}
}
@article{faucris.249332696,
abstract = {In this article, we propose an adaptive spectral graph wavelet method to solve partial differential equations on network-like structures using so-called spectral graph wavelets. The concept of spectral graph wavelets is based on the discrete graph Laplacian. The beauty of the method lies in the fact that the same operator is used for the approximation of differential operators and for the construction of the spectral graph wavelets. Two test functions on different topologies of the network are considered in order to explain the features of the spectral graph wavelet (i.e., behavior of wavelet coefficients and reconstruction error). Subsequently, the method is applied to parabolic problems on networks with different topologies. The numerical results show that the method accurately captures the emergence of the localized patterns at all the scales (including the junction of the network) and the node arrangement is accordingly adapted. The convergence of the method is verified and the efficiency of the method is discussed in terms of CPU time.},
author = {Mehra, Mani and Shukla, Ankita and Leugering, Günter},
doi = {10.1007/s10444-020-09824-9},
faupublication = {yes},
journal = {Advances in Computational Mathematics},
keywords = {Adaptive node arrangement; Network models; Spectral graph wavelet},
note = {CRIS-Team Scopus Importer:2021-02-12},
peerreviewed = {Yes},
title = {{An} adaptive spectral graph wavelet method for {PDEs} on networks},
volume = {47},
year = {2021}
}
@article{faucris.110513084,
abstract = {The problem of rational approximation is facilitated by introducing both lower and upper bounds on the denominators. For a general fractional inf-sup problem with constrained denominators, a differential correction algorithm and convergence results are given. Numerical examples are presented. The proposed algorithm has certain advantages compared with the original differential correction method: not only upper but also lower bounds for the optimal value are computed, linear convergence is always guaranteed, and due to a different start convergence is more rapid.},
author = {Gugat, Martin},
doi = {10.1007/s003659900010},
faupublication = {no},
journal = {Constructive Approximation},
keywords = {41A20; 65D15; 90C32; 90C34; Chebyshev approximation; Constrained denominators; Differential correction algorithm; Fractional programming; Rational approximation},
note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lama1.analgo},
pages = {197-221},
peerreviewed = {Yes},
title = {{An} {Algorithm} for {Chebyshev} {Approximation} by {Rationals} with {Constrained} {Denominators}},
volume = {12},
year = {1996}
}
@article{faucris.124194444,
abstract = {We consider a system of scalar nonlocal conservation laws on networks that model a highly re-entrant multi-commodity manufacturing system as encountered in semi-conductor production. Every single commodity is modeled by a nonlocal conservation law, and the corresponding PDEs are coupled via a collective load, the work m progress. We illustrate the dynamics for two commodities. In the applications, directed acyclic networks naturally occur, therefore this type of networks is considered. On every edge of the network we have a system of coupled conservation laws with nonlocal velocity. At the junctions the right hand side boundary data of the foregoing edges is passed as left hand side boundary data to the following edges and PDEs. For distributing junctions, where we have more than one outgoing edge, we impose time dependent distribution functions that guarantee conservation of mass. We provide results of regularity, existence and well-posedness of the multicommodity network model for L-P-, BV- and W-1,W-p-data. Moreover, we define an L-2-tracking type objective and show the existence of minimizers that solve the corresponding optimal control problem.},
author = {Gugat, Martin and Keimer, Alexander and Leugering, Günter and Wang, Zhiqiang},
doi = {10.3934/nhm.2015.10.749},
faupublication = {yes},
journal = {Networks and Heterogeneous Media},
keywords = {Existence of minimizers;conservation laws;multi-commodity model;conservation laws on networks;nonlocal conservation laws;optimal nodal control;optimal control of conservation laws on networks;systems of hyperbolic PDEs},
pages = {749-785},
peerreviewed = {Yes},
title = {{ANALYSIS} {OF} {A} {SYSTEM} {OF} {NONLOCAL} {CONSERVATION} {LAWS} {FOR} {MULTI}-{COMMODITY} {FLOW} {ON} {NETWORKS}},
volume = {10},
year = {2015}
}
@article{faucris.120101344,
abstract = {
There are very few results about analytic solutions of problems of optimal control with minimal *L* ^{∞} norm. In this paper, we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. We start in the zero position and consider a problem of exact control, that is, we want to reach a given terminal state in a given finite time. Our aim is to find a control with minimal *L* ^{∞} norm that steers the system to the target.

We give the analytic solution for certain classes of target points, for example, target points that are given by constant functions. For such targets with zero velocity, the analytic solution has been given by Bennighof and Boucher in Ref. 1.

}, author = {Gugat, Martin}, doi = {10.1023/A:1016091803139}, faupublication = {no}, journal = {Journal of Optimization Theory and Applications}, keywords = {Optimal Control; Wave Equation; Analytic Solution; Distributed Parameter Systems}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.analyt}, pages = {397-421}, peerreviewed = {Yes}, title = {{Analytic} {Solutions} of {L}-infinity optimal control problems for the wave equation}, volume = {114}, year = {2002} } @article{faucris.241516538, abstract = {In this paper, we propose the numerical approximation of fractional initial and boundary value problems using Haar wavelets. In contrast to the Haar wavelet methods available in literature, where the fractional derivative of the function is approximated using the Haar basis, we approximate the function and its classical derivatives using Haar basis functions. Moreover, error bounds in the approximation of fractional integrals and the fractional derivatives are derived, which depend on the index J of the approximation space VWe show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4Lc and 8Lc, where L is the length of the string and c is the wave speed. © 2011 Elsevier B.V. All rights reserved.}, author = {Gugat, Martin and Tucsnak, Marius}, doi = {10.1016/j.sysconle.2011.01.004}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Boundary feedback; Delay; Feedback stabilization of pdes; Feedback with delay; Hyperbolic pde; Past observation; String; Switching delay; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.anexam}, pages = {226-230}, peerreviewed = {Yes}, title = {{An} example for the switching delay feedback stabilization of an infinite dimensional system: {The} boundary stabilization of a string}, volume = {60}, year = {2011} } @misc{faucris.110459844, author = {Jahn, Johannes}, faupublication = {yes}, note = {UnivIS-Import:2015-03-05:Pub.1995.nat.dma.pama21.angewa}, peerreviewed = {automatic}, title = {{Angewandte} nichtlineare {Vektoroptimierung}}, year = {1995} } @article{faucris.110282524, abstract = {In this paper an interior point method is presented for nonlinear programming problems with inequality constraints. On defining a modified distance function the original problem is solved sequentially by using a method of feasible directions. At each iteration a usable feasible direction can be determined explicitly. Under certain assumptions it can be shown that every accumulation point of the sequence of points constructed by the proposed algorithm satisfies the Kuhn-Tucker conditions. © 1979 Physica-Verlag.}, author = {Jahn, Johannes}, doi = {10.1007/BF01917332}, faupublication = {no}, journal = {Mathematical Methods of Operations Research}, note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.aninte}, pages = {1-15}, peerreviewed = {Yes}, title = {{An} {Interior} {Point} {Method} for {Nonlinear} {Programming}}, volume = {23}, year = {1979} } @article{faucris.117450344, abstract = {We consider an exact boundary control problem for the wave equation with given initial and terminal data and Dirichlet boundary control. The aim is to steer the state of the system that is defined on a given domain to a position of rest in finite time. The optimal control that is obtained as the solution of the problem depends on the data that define the problem, in particular on the domain. Often for the numerical solution of the control problem, this given domain is replaced by a polygon. This is the motivation to study the convergence of the optimal controls for the polygon to the optimal controls for the given domain. To study the convergence, the values of the optimal controls that are defined on the boundaries of the approximating polygons are mapped in the normal directions of the polygon to control functions defined on the boundary of the original domain. This map has already been used by Bramble and King, Deckelnick, Guenther and Hinze and by Casas and Sokolowski. Using this map, we can show the strong convergence of the transformed controls as the polygons approach the given domain. An essential tool to obtain the convergence is a regularization term in the objective functions to increase the regularity of the state.}, author = {Gugat, Martin and Sokolowski, Jan}, doi = {10.1080/00036811.2012.724404}, faupublication = {yes}, journal = {Applicable Analysis}, keywords = {wave equation; Dirichlet boundary control; exact control; optimal control; domain sensitivity; polygonal domain; 49J20; 35L05; 35L53}, note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.lama1.anoteo}, pages = {2200-2214}, peerreviewed = {Yes}, title = {{A} note on the approximation of {Dirichlet} boundary control problems for the wave equation on curved domains}, url = {http://www.tandfonline.com/doi/abs/10.1080/00036811.2012.724404}, volume = {92}, year = {2012} } @article{faucris.255804887, abstract = {In this paper we discuss some issues related to Poincaré’s inequality for a special class of weighted Sobolev spaces. A common feature of these spaces is that they can be naturally associated with differential operators with variable diffusion coefficients that are not uniformly elliptic. We give a classification of these spaces in the 1-D case bases on a measure of degeneracy of the corresponding weight coefficient and study their key properties.}, author = {Kogut, Peter I. and Kupenko, Olha P. and Leugering, Günter and Wang, Yue}, doi = {10.15421/141905}, faupublication = {yes}, journal = {Journal of Optimization, Differential Equations and Their Applications}, keywords = {Degenerate equation; Poincaré’s inequality; Weighted Sobolev spaces}, note = {CRIS-Team Scopus Importer:2021-04-20}, pages = {1-22}, peerreviewed = {Yes}, title = {{A} {NOTE} on {WEIGHTED} {SOBOLEV} {SPACES} {RELATED} to {WEAKLY} and {STRONGLY} {DEGENERATE} {DIFFERENTIAL} {OPERATORS}}, volume = {27}, year = {2019} } @article{faucris.119326284, abstract = {

In this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.

}, author = {Lindenberger, Christoph and Pflug, Lukas and Hübner, Holger and Buchholz, Rainer}, doi = {10.1007/s12257-011-0371-5}, faupublication = {yes}, journal = {Biotechnology and Bioprocess Engineering}, keywords = {baculovirus; modelling; insect cells; infection cycle}, pages = {211-217}, peerreviewed = {Yes}, title = {{A} novel model for studying baculovirus infection process}, url = {http://link.springer.com/article/10.1007/s12257-011-0371-5}, volume = {17}, year = {2012} } @article{faucris.119922044, abstract = {A model comprised of a nonlinear von Karman plate coupled with a nonlinear beam equation is developed from first principles. Dynamic junction conditions are imposed at the interface. Wellposedness is established by first considering a corresponding linear problem, then applying a perturbation theorem for nonlinear semigroups. Proof of regularity takes advantage of elliptic theory, as well as the regularity of the Airy's stress function. The compatibility constraints at the junction give rise to mathematical challenges not seen in earlier work on the individual plate and beam models. (C) 2005 Elsevier Ltd. All rights reserved.}, author = {Leugering, Günter and Horn, Mary Ann}, doi = {10.1016/j.na.2005.01.048}, faupublication = {yes}, journal = {Nonlinear Analysis - Theory Methods & Applications}, keywords = {Plate-beam model;Nonlinear dynamics;Existence and uniqueness}, pages = {E1529-E1539}, peerreviewed = {Yes}, title = {{An} overview of modelling challenges for a nonlinear plate-beam model}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X05000647}, volume = {63}, year = {2005} } @article{faucris.115613344, abstract = {In this paper we consider the behaviour of the multipliers for one-parametric semi-infinite programs near critical parameters, where the Mangasarian-Fromovitz constraint qualification can be violated. The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers. © Springer-Verlag 1999.}, author = {Gugat, Martin}, doi = {10.1007/s10107990058a}, faupublication = {no}, journal = {Mathematical Programming}, keywords = {Gauvin's theorem; Karush-Kuhn-Tucker multiplier; Mangasarian-Fromovitz constraint qualification; Modulus of multiplier growth; Parametric nonconvex program; Semi-infinite program; Singular parameters; Uniform Mangasarian-Fromovitz condition}, note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.lama1.aparam}, pages = {643-653}, peerreviewed = {Yes}, title = {{A} parametric view on the {Mangasarian}-{Fromovitz} constraint qualification}, volume = {85}, year = {1999} } @article{faucris.117897384, abstract = {We consider a boundary optimal control problem for the acoustic wave equation with a final value cost criterion. A time-domain decomposition procedure for the corresponding optimality system is introduced, which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. The process is inherently parallel and is suitable for real-time control applications. Convergence of the local solutions and controls to the global ones was established in an earlier publication. In this paper, a posteriori error estimates of the difference between the local solutions and the global one are obtained in terms of the mismatch of the nth iterates, or of successive iterates, across the time-domain break points.}, author = {Leugering, Günter and Langnese, John E.}, doi = {10.1007/s00245-002-0750-6}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, keywords = {acoustic wave equation;optimal control;domain decomposition;a posteriori error estimates}, pages = {263-290}, peerreviewed = {Yes}, title = {{A} posteriori error estimates in time-domain decomposition of final value optimal control of the acoustic wave equation}, url = {http://link.springer.com/article/10.1007/s00245-002-0750-6}, volume = {46}, year = {2002} } @incollection{faucris.121142824, address = {New York}, author = {Jahn, Johannes and Krabs, W.}, booktitle = {Multicriteria Optimization in Engineering and in the Sciences}, editor = {W. Stadler}, faupublication = {yes}, note = {UnivIS-Import:2015-04-17:Pub.1988.nat.dma.pama21.applic}, pages = {49-75}, peerreviewed = {unknown}, publisher = {Plenum Press}, title = {{Applications} of {Multicriteria} {Optimization} in {Approximation} {Theory}}, year = {1988} } @article{faucris.123696804, abstract = {We study a Dirichlet optimal control problem for a quasi-linear monotone elliptic equation, the so-called weighted p-Laplacian problem. The coefficient of the -Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the control such that there is a strictly positive lower and some upper bound. In order to handle the inherent degeneracy of the -Laplacian, we use a regularization, sometimes referred to as the -Laplacian. We derive existence and uniqueness of solutions to the underlying boundary value problem and the optimal control problem. In fact, we introduce a two-parameter model for the weighted -Laplacian, where we approximate the nonlinearity by a bounded monotone function, parametrized by κ. Further, we discuss the asymptotic behavior of the solutions to the regularized problem on each (ϵ, κ)-level as the parameters tend to zero and infinity, respectively.}, author = {Casas, Eduardo and Kogut, Peter I. and Leugering, Günter}, doi = {10.1137/15M1028108}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {Control in coefficients; Nonlinear Dirichlet problem; Optimal control}, pages = {1406-1422}, peerreviewed = {Yes}, title = {{Approximation} of optimal control problems in the coefficient for the p-{Laplace} equation. {I}. {Convergence} result}, volume = {54}, year = {2016} } @article{faucris.120697544, abstract = {We consider the approximation of semigroups e
In this paper we consider the flow through a frictionless horizontal rectangular channel that is governed by de St. Venant equations and show that the state can be controlled in finite time from a stationary initial state to a given stationary terminal state in such a way that during this transition, the state stays in the class of C *L*_{2}-boundary controls. Accordingly, we present a result on approximative controllability. The method is general.},
author = {Leugering, Günter and Schmidt, E. J. P. Georg},
doi = {10.1002/mma.1670110502},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
pages = {573-586},
peerreviewed = {Yes},
title = {{BOUNDARY} {CONTROL} {OF} {A} {VIBRATING} {PLATE} {WITH} {INTERNAL} {DAMPING}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670110502/abstract},
volume = {11},
year = {1989}
}
@article{faucris.117346944,
abstract = {In the application of feedback controls, a delay may appear as a perturbation caused by the computation of the controls. For vibrating systems, this delay can destroy the stabilizing effect of the control. To avoid this problem, we consider feedback laws where a certain delay is included as a part of the control law and not as a perturbation. We consider systems that are governed by the wave equation. As a first system, we consider a string that is fixed at one end and stabilized with a boundary feedback with constant delay at the other end. As a second example, we consider a circular string where both ends of the string are coupled by a feedback law. For both systems, we show the exponential stability of the proposed feedback with retarded input. Moreover, for the first system, we show robustness with respect to variations in time of the feedback parameter. The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.2010 © The author 2010. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.},
author = {Gugat, Martin},
doi = {10.1093/imamci/dnq007},
faupublication = {yes},
journal = {IMA Journal of Mathematical Control and Information},
keywords = {boundary feedback; circular string; delay; feedback stabilization of partial differential equations; feedback with delay; hyperbolic partial differential equation; past observation; time-dependent feedback parameter; wave equation},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.bounda},
pages = {189-203},
peerreviewed = {Yes},
title = {{Boundary} feedback stabilization by time delay for one-dimensional wave equations},
url = {http://imamci.oxfordjournals.org/cgi/content/abstract/dnq007?ijkey=gGdKiGMBG9950h8&keytype=ref},
volume = {27},
year = {2010}
}
@article{faucris.247775816,
abstract = {In this work we address the problem of boundary feedback stabilization for a geometrically exact shearable beam, allowing for large deflections and rotations and small strains. The corresponding mathematical model may be written in terms of displacements and rotations (geometrically exact beam), or intrinsic variables (intrinsic geometrically exact beam). A nonlinear transformation relates both models, allowing us to take advantage of the fact that the latter model is a one-dimensional first-order semilinear hyperbolic system, and deduce stability properties for both models. By applying boundary feedback controls at one end of the beam while the other end is clamped, we show that the zero steady state of the intrinsic geometrically exact beam model is locally exponentially stable for the H-1- and H-2 norms. The proof rests on the construction of a Lyapunov function, where the theory of Bastin and Coron [Stability and Boundary Stabilization of 1-D Hyperbolic Systems, in Progr. Nonlinear Differential Equations Appl. 88, Birkhauser/Springer, Cham, 2016] plays a crucial role. The major difficulty in applying this theory stems from the complicated nature of the nonlinearity and lower order term where no smallness arguments apply. Using the relationship between both models, we deduce the existence of a unique solution to the geometrically exact beam model, and properties of this solution as time goes to +infinity.},
author = {Rodriguez, Charlotte and Leugering, Günter},
doi = {10.1137/20M1340010},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
month = {Jan},
note = {CRIS-Team WoS Importer:2021-01-15},
pages = {3533-3558},
peerreviewed = {Yes},
title = {{BOUNDARY} {FEEDBACK} {STABILIZATION} {FOR} {THE} {INTRINSIC} {GEOMETRICALLY} {EXACT} {BEAM} {MODEL}},
volume = {58},
year = {2020}
}
@article{faucris.261333644,
abstract = {The flow of gas through a pipeline network can be modelled by a coupled system of 1-d quasilinear hyperbolic equations. In this system, the influence of certain source terms that model friction effects is essential. Often for the solution of control problems it is convenient to replace the quasilinear model by a simpler semilinear model. In this paper, we analyze the behavior of such a semilinear model on a star-shaped network. The model is derived from the diagonal form of the quasilinear model by replacing the eigenvalues by the sound speed multiplied by 1 or -1 respectively. Thus in the corresponding eigenvalues the influence of the gas velocity is neglected, which is justified in the applications since it is much smaller than the sound speed in the gas. For a star-shaped network of horizontal pipes for suitable coupling conditions we present boundary feedback laws that stabilize the system state exponentially fast to a position of rest for sufficiently small initial data. We show the exponential decay of the L2-norm for arbitrarily long pipes. This is remarkable since in general even for linear systems, for certain source terms the system can become exponentially unstable if the space interval is too long. Our proofs are based upon an observability inequality and suitably chosen Lyapunov functions. At the end of the paper, numerical examples are presented that include a comparison of the semilinear model and the quasilinear system. },
author = {Gugat, Martin and Giesselmann, Jan},
doi = {10.1051/cocv/2021061},
faupublication = {yes},
journal = {Esaim-Control Optimisation and Calculus of Variations},
keywords = {Dirichlet feedback; Exponential stability; Isothermal Euler equations; Observability inequality; Pipeline networks; Real gas; Riemann invariants; Semilinear model; Source terms; Stabilization},
note = {CRIS-Team Scopus Importer:2021-07-09},
peerreviewed = {Yes},
title = {{Boundary} feedback stabilization of a semilinear model for the flow in star-shaped gas networks},
volume = {27},
year = {2021}
}
@article{faucris.114066964,
abstract = {The Schlögl system is governed by a nonlinear reaction-diffusion partial differential equation with a cubic nonlinearity that determines three constant equilibrium states. It is a classical example of a chemical reaction system that is bistable. The constant equilibrium that is enclosed by the other two constant equilibrium points is unstable. In this paper, Robin boundary feedback laws are presented that stabilize the system in a given stationary state or more generally in a given time-dependent desired system orbit. The exponential stability of the closed loop system with respect to the ^{L2}-norm is proved. In particular, it is shown that with the boundary feedback law the unstable constant equilibrium point can be stabilized.},
author = {Gugat, Martin and Tröltzsch, Fredi},
doi = {10.1016/j.automatica.2014.10.106},
faupublication = {yes},
journal = {Automatica},
keywords = {Boundary feedback; Exponential stability; Lyapunov function; Parabolic partial differential equation; Periodic operation; Poincaré-Friedrichs inequality; Robin feedback; Stabilization of desired orbits; Stabilization of periodic orbits},
month = {Jan},
note = {UnivIS-Import:2015-03-09:Pub.2015.nat.dma.zentr.bounda},
pages = {192-199},
peerreviewed = {Yes},
title = {{Boundary} feedback stabilization of the {Schlögl} system},
volume = {51},
year = {2015}
}
@article{faucris.113899544,
abstract = {We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small. © 2014 Elsevier B.V. All rights reserved.},
author = {Gugat, Martin},
doi = {10.1016/j.sysconle.2014.01.007},
faupublication = {yes},
journal = {Systems & Control Letters},
keywords = {Anti-damping; Boundary feedback; Damping; Decay rate; Exponential stability; Hyperbolic partial differential equation; Nonlinear wave equation; Semilinear wave equation; Telegraph equation},
note = {UnivIS-Import:2015-03-09:Pub.2014.nat.dma.lama1.bounda},
pages = {72-84},
peerreviewed = {Yes},
title = {{Boundary} feedback stabilization of the telegraph equation: {Decay} rates for vanishing damping term},
url = {http://ac.els-cdn.com/S0167691114000279/1-s2.0-S0167691114000279-main.pdf?{\_}tid=631b42fa-9efc-11e3-83ef-00000aab0f26&acdnat=1393429438{\_}c7a54e1446ab014020ff9d6d7536964a},
volume = {66},
year = {2014}
}
@article{faucris.201253582,
author = {Gugat, Martin and Rosier, Lionel and Perrolaz, Vincent},
doi = {10.1007/s00028-018-0449-z},
faupublication = {yes},
journal = {Journal of Evolution Equations},
peerreviewed = {Yes},
title = {{Boundary} stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms},
url = {https://link.springer.com/article/10.1007/s00028-018-0449-z},
year = {2018}
}
@inproceedings{faucris.121010164,
author = {Rathmann, Wigand and Vogel, Frank and Landes, Hermann and Kaltenbacher, Manfred},
booktitle = {21. CAD-FEM Users' Meeting},
faupublication = {no},
peerreviewed = {No},
publisher = {CAD-FEM GmbH Grafing},
title = {{Calculation} of {Sound} {Fields} in {Flowing} {Media} {Using} {CAPA} and {Diffpack}},
year = {2003}
}
@incollection{faucris.111139424,
abstract = {We consider optimal control problems for the flow of gas or fresh water in pipe networks as well as drainage or sewer systems in open canals. The equations of motion are taken to be represented by the nonlinear isothermal Euler gas equations, the water hammer equations, or the St. Venant equations for flow. We formulate model hierarchies and derive an abstract model for such network flow problems including pipes, junctions, and controllable elements such as valves, weirs, pumps, as well as compressors. We use the abstract model to give an overview of the known results and challenges concerning equilibria, well-posedness, controllability, and optimal control. A major challenge concerning the optimization is to deal with switching on-off states that are inherent to controllable devices in such applications combined with continuous simulation and optimization of the gas flow. We formulate the corresponding mixed-integer nonlinear optimal control problems and outline a decomposition approach as a solution technique.},
address = {Singapore},
author = {Hante, Falk and Leugering, Günter and Martin, Alexander and Schewe, Lars and Schmidt, Martin},
booktitle = {Industrial Mathematics and Complex Systems: Emerging Mathematical Models, Methods and Algorithms},
doi = {10.1007/978-981-10-3758-0{\_}5},
editor = {Manchanda, Pammy; Lozi, René; Siddiqi, Abul Hasan},
faupublication = {yes},
isbn = {978-981-10-3758-0},
keywords = {Networks, pipes, canals, Euler and St. Venant equations, hierarchy of models, domain decomposition, controllability, optimal control.},
pages = {77-122},
peerreviewed = {unknown},
publisher = {Springer Singapore},
series = {Industrial and Applied Mathematics},
title = {{Challenges} in {Optimal} {Control} {Problems} for {Gas} and {Fluid} {Flow} in {Networks} of {Pipes} and {Canals}: {From} {Modeling} to {Industrial} {Applications}},
url = {https://opus4.kobv.de/opus4-trr154/files/121/isiam-paper.pdf},
year = {2017}
}
@article{faucris.112244264,
abstract = {We consider the subcritical flow in gas networks consisting of a finite linear sequence of pipes coupled by compressor stations. Such networks are important for the transportation of natural gas over large distances to ensure sustained gas supply. We analyse the system dynamics in terms of Riemann invariants and study stationary solutions as well as classical non-stationary solutions for a given finite time interval. Furthermore, we construct feedback laws to stabilize the system locally around a given stationary state. To do so we use a Lyapunov function and prove exponential decay with respect to the L^{2}-norm. © American Institute of Mathematical Sciences.},
author = {Hirsch-Dick, Markus and Gugat, Martin and Leugering, Günter},
doi = {10.3934/nhm.2010.5.691},
faupublication = {yes},
journal = {Networks and Heterogeneous Media},
keywords = {Classical solutions; Critical length; Feedback law; Gas networks; Gun barrel; Linear networks; Lyapunov function; Networked hyperbolic systems; Riemann invariants},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.classi},
pages = {691-709},
peerreviewed = {Yes},
title = {{Classical} solutions and feedback stabilization for the gas flow in a sequence of pipes},
url = {http://aimsciences.org/journals/displayArticles.jsp?paperID=5645},
volume = {5},
year = {2010}
}
@article{faucris.112749824,
abstract = {Compressible squeeze film damping is a phenomenon of great importance for micromachines. For example, for the optimal design of an electrostatically actuated micro-cantilever mass sensor that operates in air, it is essential to have a model for the system behavior that can be evaluated efficiently. An analytical model that is based upon a solution of the linearized Reynolds equation has been given by R.B. Darling. In this paper we explain how some infinite sums that appear in Darling’s model can be evaluated analytically. As an example of applications of these closed form representations, we compute an approximation for the critical frequency where the spring component of the reaction force on the microplate, due to the motion through the air, is equal to a certain given multiple of the damping component. We also show how some double series that appear in the model can be reduced to a single infinite series that can be approximated efficiently.},
author = {Gugat, Martin},
doi = {10.3390/app2020479},
faupublication = {yes},
journal = {Applied Sciences},
keywords = {squeeze film; optimal sensor design; resonant mass sensor; double series; efficient approximation of double series; evaluation of infinite series; Darling’s model},
note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.zentr.closed},
pages = {479-484},
peerreviewed = {unknown},
title = {{Closed} {Form} {Representations} of {Some} {Series} in {Darling}s {Model} for {Squeeze} {Film} {Damping} with a {Rectangular} {Plate}},
url = {http://www.mdpi.com/2076-3417/2/2/479},
volume = {2},
year = {2012}
}
@misc{faucris.118869344,
abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport
optimization problems. As mixed-integer reformulations of pooling-type
mixing models already render small-size instances computationally
intractable, we investigate the applicability of smooth nonlinear
programming techniques for equivalent complementarity-based
reformulations. Based on recent results for remodeling piecewise affine
constraints using an inverse parametric quadratic programming approach,
we show that classical stationarity concepts are meaningful for the
resulting complementarity-based reformulation of the mixing equations.
Further, we investigate in a numerical study the performance of this
reformulation compared to a more compact complementarity-based one that
does not feature such beneficial regularity properties. All computations
are performed on publicly available data of real-world size problem
instances from steady-state gas transport.},
author = {Hante, Falk and Schmidt, Martin},
faupublication = {yes},
keywords = {Gas transport networks, Mixing, Inverse parametric quadratic programming, Complementarity constraints, MPCC},
peerreviewed = {automatic},
title = {{Complementarity}-{Based} {Nonlinear} {Programming} {Techniques} for {Optimal} {Mixing} in {Gas} {Networks}},
url = {http://www.optimization-online.org/DB{\_}HTML/2017/09/6198.html},
year = {2017}
}
@article{faucris.220859888,
abstract = {We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we show that classical stationarity concepts are meaningful for the resulting complementarity-based reformulation of the mixing equations. Further, we investigate in a numerical study the performance of this reformulation compared to a more compact complementarity-based one that does not feature such beneficial regularity properties. All computations are performed on publicly available data of real-world size problem instances from steady-state gas transport.},
author = {Hante, Falk and Schmidt, Martin},
doi = {10.1007/s13675-019-00112-w},
faupublication = {yes},
journal = {EURO Journal on Computational Optimization},
keywords = {Complementarity constraints; Gas transport networks; Inverse parametric quadratic programming; Mixing; MPCC},
note = {CRIS-Team Scopus Importer:2019-06-18},
peerreviewed = {Yes},
title = {{Complementarity}-based nonlinear programming techniques for optimal mixing in gas networks},
year = {2019}
}
@article{faucris.111644544,
author = {Knossalla, Martin},
faupublication = {yes},
journal = {Journal of Nonlinear and Variational Analysis},
pages = {265-279},
peerreviewed = {Yes},
title = {{Concepts} on generalized epsilon-subdifferentials for minimizing locally {Lipschitz} continuous functions},
url = {http://jnva.biemdas.com/archives/404},
year = {2017}
}
@article{faucris.116673304,
abstract = {

`We consider models based on conservation laws. For the optimization of`

`such systems, a sensitivity analysis is essential to determine how changes in the decision`

`variables influence the objective function. Here we study the sensitivity with respect`

`to the initial data of objective functions that depend upon the solution of Riemann`

`problems with piecewise linear flux functions. We present representations for the one–`

`sided directional derivatives of the objective functions. The results can be used in the`

`numerical method called Front-Tracking.`

The LMS Moodle and ILIAS are widely used at universities and Universities of Applied

Sciences. But even nowadays, it is still a challenge to use the possibilities given by digital

materials to create learning content which offers more than a classical textbook. Several

tools are available to show, explain and dynamically explore mathematical concepts,

among them are CoCalc (former SageMathCloud), SageCell, CDF-Player, JSXGraph and

GeoGebra. It is still quite common that content for a lecture is provided inside the local

LMS, while the learner has to open another platform or software to use the dynamic

mathematical tools for exploration of the content. In our contribution (talk or poster) we

will show our approaches to include dynamic mathematics inside LMS.

In particular, we use JSXGraph for dynamic 2D diagrams and the SageMathCell for a wide

range of mathematical aspects. JSXGraph is a JavaScript library, which is quite easy to use

and which offers the possibility to include user interactions via HTML-forms. The

advantage is that the computations are done in the browser on client-side. On the other

hand, SageMathCell has a huge variety of tools already included, like Maxima, R, Octave

or Python. Furthermore, it is very easy to show 3D-diagrams. This is made possible by

executing the computation on a remote server, which has to be connected from the content.

We include JSXGraph and SageMathCell in classical HTML-Pages as media content and

through dedicated plug-ins for the LMS Moodle and ILIAS. During the ”Mathematics for

Engineers” (part 1-3) we provide additional material for several topics, e.g. series, (un)-

constrained optimization, integration, parametrization of curves and surfaces or differential

equations. We see the advantage that the diagrams will become an integral part of the

learning modules and the learning unit does not look like patchwork.

Further, the learners can focus on the content and do not have to bring additional software

or to login in a second learning platform. During presence lectures the lecturer can use the

same LMS as the learnersdo for their follow-up work.

For JSXGraph, there is a plug-in for Moodle, for the usage of SageMathCell inside ILIAS

the first author could initiate the development.

An integrodifferential equation of the Volterra type is considered under the action of an

}, author = {Leugering, Günter}, doi = {10.1007/BF01442653}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {223-250}, peerreviewed = {Yes}, title = {{EXACT} {BOUNDARY} {CONTROLLABILITY} {OF} {AN} {INTEGRODIFFERENTIAL} {EQUATION}}, url = {http://link.springer.com/article/10.1007/BF01442653}, volume = {15}, year = {1987} } @article{faucris.227770910, abstract = {The exact boundary controllability for hyperbolic systems can not be realized generally on a network with loops (see [16]). In this paper we consider the exact boundary controllability of nodal profile on a network with loops. Precisely speaking, on a network with a triangle-like loop, when nodal profiles are given at various kinds of nodes, different constructive methods can be used to get the corresponding exact boundary controllability of nodal profile for Saint-Venant system by means of boundary controls acting on suitable nodes, respectively. This reveals that the exact boundary controllability of nodal profile is quite different from the usual exact boundary controllability, and has relatively distinctive behaviors and characters. (C) 2018 Elsevier Masson SAS. All rights reserved.}, author = {Zhuang, Kaili and Leugering, Günter and Li, Tatsien}, doi = {10.1016/j.matpur.2018.10.001}, faupublication = {yes}, journal = {Journal De Mathematiques Pures Et Appliquees}, note = {CRIS-Team WoS Importer:2019-10-11}, pages = {34-60}, peerreviewed = {Yes}, title = {{Exact} boundary controllability of nodal profile for {Saint}-{Venant} system on a network with loops}, volume = {129}, year = {2019} } @article{faucris.262156508, abstract = {Based on the theory of exact boundary controllability of nodal profile for hyperbolic systems, the authors propose the concept of exact boundary controllability of partial nodal profile to expand the scope of applications. With the new concept, we can shorten the controllability time, save the number of controls, and increase the number of charged nodes with given nodal profiles. Furthermore, we introduce the concept of in-situ controlled node to deal with a new situation that one node can be charged and controlled simultaneously. The minimum number of boundary controls on the entire tree-like network is determined by using the concept of ‘degree of freedom of charged nodes’ introduced. And the concept of ‘control path’ is introduced to appropriately divide the network, so that we can determine the infimum of controllability time. General frameworks of constructive proof are given on a single interval, a star-like network, a chain-like network and a planar tree-like network for linear wave equation(s) with Dirichlet, Neumann, Robin and dissipative boundary conditions to establish a complete theory on the exact boundary controllability of partial nodal profile.}, author = {Wang, Yue and Li, Tatsien}, doi = {10.1016/j.nonrwa.2021.103383}, faupublication = {yes}, journal = {Nonlinear Analysis-Real World Applications}, keywords = {Control path; Exact boundary controllability; Partial nodal profile; Piecewise C; Planar tree-like network; The degree of freedom of charged node}, note = {CRIS-Team Scopus Importer:2021-07-30}, peerreviewed = {Yes}, title = {{Exact} boundary controllability of partial nodal profile for network of strings}, volume = {62}, year = {2021} } @article{faucris.119702924, abstract = {This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li, T. T., Controllability and Observability for Quasilinear Hyperbolic Systems, AIMS Ser. Appl. Math., vol 3, American Institute of Mathematical Sciences and Higher Education Press, 2010] existing in a neighborhood of the equilibrium solution. The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.}, author = {Leugering, Günter and Li, Tatsien and Gu, Qilong}, doi = {10.1007/s11401-017-1092-7}, faupublication = {yes}, journal = {Chinese Annals of Mathematics. Series B}, keywords = {Exact boundary controllability; Nonlinear Timoshenko beams; Semi-global classical solutions; Tree-like networks}, pages = {711-740}, peerreviewed = {unknown}, title = {{Exact} boundary controllability on a tree-like network of nonlinear planar {Timoshenko} beams}, volume = {38}, year = {2017} } @article{faucris.117905084, abstract = {Distributed load control of motions governed by an abstract partial integrodifferential equation is studied. First a new system-theoretic approach to a mild solution theory of equations arising in viscoelasticity of fading memory type is developed. Then it is shown that control results for the damped abstract wave equation devolve to a special class of “virgin” material with fading memory.}, author = {Leugering, Günter}, doi = {10.1080/00036818408839521}, faupublication = {no}, journal = {Applicable Analysis}, keywords = {93B05; 45K05; 73K05}, month = {Jan}, pages = {221-243}, peerreviewed = {Yes}, title = {{EXACT} {CONTROLLABILITY} {IN} {VISCOELASTICITY} {OF} {FADING} {MEMORY} {TYPE}}, url = {http://www.tandfonline.com/doi/abs/10.1080/00036818408839521}, volume = {18}, year = {1984} } @article{faucris.121753104, abstract = {We study optimal control problems for linear systems with prescribed initial and terminal states. We analyze the exact penalization of the terminal constraints. We show that for systems that are exactly controllable, the norm-minimal exact control can be computed as the solution of an optimization problem without terminal constraint but with a nonsmooth penalization of the end conditions in the objective function, if the penalty parameter is sufficiently large. We describe the application of the method for hyperbolic and parabolic systems of partial differential equations, considering the wave and heat equations as particular examples. Copyright © 2016 John Wiley & Sons, Ltd.}, author = {Gugat, Martin and Zuazua, Enrique}, doi = {10.1002/oca.2238}, faupublication = {yes}, journal = {Optimal Control Applications & Methods}, keywords = {exact controllability;optimal control;terminal constraint;exact penalization;wave equation;heat equation;moment equations;method of moments;L1 optimal control;abstract Cauchy problems;nonsmooth optimization}, peerreviewed = {Yes}, title = {{Exact} penalization of terminal constraints for optimal control problems}, url = {http://onlinelibrary.wiley.com/doi/10.1002/oca.2238/abstract}, volume = {37}, year = {2016} } @inproceedings{faucris.263538379, abstract = {In this paper, we study the time-fractional diffusion equation on a metric star graph. The existence and uniqueness of the weak solution are investigated and the proof is based on eigenfunction expansions. Some priori estimates and regularity results of the solution are proved.}, author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter}, booktitle = {Communications in Computer and Information Science}, date = {2020-09-10/2020-09-12}, doi = {10.1007/978-981-16-4772-7{\_}2}, editor = {Ashish Awasthi, Sunil Jacob John, Satyananda Panda}, faupublication = {yes}, isbn = {9789811647710}, keywords = {Caputo fractional derivative; Star graph; Time-fractional diffusion equation; Weak solution}, note = {CRIS-Team Scopus Importer:2021-09-03}, pages = {25-41}, peerreviewed = {unknown}, publisher = {Springer Science and Business Media Deutschland GmbH}, title = {{Existence} and {Uniqueness} of {Time}-{Fractional} {Diffusion} {Equation} on a {Metric} {Star} {Graph}}, venue = {Virtual, Online}, volume = {1345}, year = {2021} } @article{faucris.217952993, abstract = {In this paper, we study a nonlinear Caputo fractional boundary value problem on a star graph. By means of transformation, an equivalent system of fractional boundary value problem is obtained. Then we establish the existence and uniqueness results by fixed point theory: in particular, using Banach's contraction principle and Schaefer's fixed point theorem. We also present some examples to illustrate the application of our results.}, author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter}, doi = {10.1016/j.jmaa.2019.05.011}, faupublication = {yes}, journal = {Journal of Mathematical Analysis and Applications}, keywords = {Boundary value problem; Caputo fractional derivative; Differential equation on graphs; Fixed point theorems}, note = {CRIS-Team Scopus Importer:2019-05-21}, peerreviewed = {Yes}, title = {{Existence} and uniqueness results for a nonlinear {Caputo} fractional boundary value problem on a star graph}, year = {2019} } @article{faucris.122946824, abstract = {We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the

For master students of the process technology and energy technology we offer a course on simulation of transport processes. Two aims are focused:

The students should learn or repeat the basics in using a simulation tools.

They should learn to combine specialized knowledge with mathematical concepts to simulate a technical process.

In the first part of the course the students collect first experiences in programming by modeling a Rankine cycle using Matlab. Hereby they discuss the quality of the presented mathematical model and possible improvements. The students are accompanied by the lecturers of the lecture "Transport processes" (master studies) and “Mathematics for Engineers” (bachelor studies). While working on the computer learners can discuss their questions, programming ideas and difficulties with each other and the trainers and they receive immediate feedbacks. The second part of the course is focuses on simple heat transfer processes described by ODE or PDE models. Therefore some mathematical concepts (e.g. linear equation systems) are needed, but they have learned it about three years ago.

Up to now the mathematical models of the technical processes and the repetition of the mathematical basics were presented as talks during the lectures with little time remained for the discussion. But the students need enough time to reconsider the introduced topics. We have seen, that this process needs more time then scheduled, e.g. to understand the way to describe the first derivative of a function on a interval by a system of linear equation system.

Now we are working on a didactic reorganization (flipped classroom) of our course, so that the students will have enough time, to repeat subjects needed in our course.

Therefore on-line learning modules and formative on-line tests have to be finished to prepare the single sessions. Thus questions can be discussed quite early and it remains more time to discuss, e.g. improvements of the models. By using the flipped classroom concept the students will be motivated to work more independently and they may reach a better understanding by using the digital learning materials as starting point for the considerations. Thus we will generate a more active participation in the teaching and learning events and better learner’s results can be achieved.

In my talk I would like to discuss these ideas and I will give a short status report of the actual course.

}, author = {Rathmann, Wigand and Wensing, Michael and Zepf, Stefanie}, booktitle = {The 18th SEFI Mathematics working Group Seminar}, date = {2016-06-27/2016-06-29}, faupublication = {yes}, peerreviewed = {unknown}, title = {{Flipped} classroom in interdisciplinary course}, url = {http://www.math.chalmers.se/SEFIMWG2016/Book%20of%20accepted%20abstracts/part49.htm}, venue = {Gothenburg}, year = {2016} } @article{faucris.117348704, abstract = {We consider a network of pipelines where the flow is controlled by a number of compressors. The consumer demand is described by desired boundary traces of the system state. We present conditions that guarantee the existence of compressor controls such that after a certain finite time the state at the consumer nodes is equal to the prescribed data. We consider this problem in the framework of continuously differentiable states. We give an explicit construction of the control functions for the control of compressor stations in gas distribution networks. Copyright © 2010 John Wiley & Sons, Ltd.}, author = {Gugat, Martin and Herty, Michael and Schleper, Veronika}, doi = {10.1002/mma.1394}, faupublication = {yes}, journal = {Mathematical Methods in the Applied Sciences}, keywords = {exact controllability;nodal control of networked hyperbolic systems;nodal profile control;classical solutions}, note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.flowco}, pages = {745-757}, peerreviewed = {Yes}, title = {{Flow} control in gas networks: {Exact} controllability to a given demand}, url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1394/abstract}, volume = {34}, year = {2010} } @incollection{faucris.119059864, address = {Heidelberg}, author = {Eichfelder, Gabriele and Jahn, Johannes}, booktitle = {Nonlinear Analysis and Variational Problems}, editor = {P.M. Pardalos, T.M. Rassias, A.A. Khan}, faupublication = {yes}, isbn = {978-1-4419-0157-6}, note = {UnivIS-Import:2015-04-20:Pub.2009.nat.dma.zentr.founda}, pages = {259-284}, peerreviewed = {No}, publisher = {Springer}, title = {{Foundations} of {Set}-{Semidefinite} {Optimization}}, url = {http://www.springer.com/mathematics/applications/book/978-1-4419-0157-6}, year = {2010} } @article{faucris.247573907, abstract = {In this paper, we study optimal control problems for nonlinear fractional order boundary value problems on a star graph, where the fractional derivative is described in the Caputo sense. The adjoint state and the optimality system are derived for fractional optimal control problem (FOCP) by using the Lagrange multiplier method. Then, the existence and uniqueness of solution of the adjoint equation is proved by means of the Banach contraction principle. We also present a numerical method to find the approximate solution of the resulting optimality system. In the proposed method, the L2 scheme and the GrUnwald-Letnikov formula is used for the approximation of the Caputo fractional derivative and the right Riemann-Liouville fractional derivative, respectively, which converts the optimality system into a system of linear algebraic equations. Two examples are provided to demonstrate the feasibility of the numerical method.}, author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter}, doi = {10.3934/mcrf.2020033}, faupublication = {yes}, journal = {Mathematical Control and Related Fields}, note = {CRIS-Team WoS Importer:2021-01-08}, pages = {189-209}, peerreviewed = {Yes}, title = {{FRACTIONAL} {OPTIMAL} {CONTROL} {PROBLEMS} {ON} {A} {STAR} {GRAPH}: {OPTIMALITY} {SYSTEM} {AND} {NUMERICAL} {SOLUTION}}, volume = {11}, year = {2021} } @inproceedings{faucris.108413624, author = {Rathmann, Wigand and Vogel, Frank and Ritter, Stefan}, booktitle = {19. CAD-FEM User's Meeting}, faupublication = {no}, peerreviewed = {No}, title = {{Free} {Form} {Shape} {Shell} {Optimization}}, year = {2001} } @inproceedings{faucris.117639104, abstract = {In this article, we present the Free Material Optimization (FMO) problem for plates and shells based on Naghdi's shell model. In FMO - a branch of structural optimization - we search for the ultimately best material properties in a given design domain loaded by a set of given forces. The optimization variable is the full material tensor at each point of the design domain. We give a basic formulation of the problem and prove existence of an optimal solution. Lagrange duality theory allows to identify the basic problem as the dual of an infinite-dimensional convex nonlinear semidefinite program. After discretization by the finite element method the latter problem can be solved using a nonlinear SDP code. The article is concluded by a few numerical studies.}, author = {Gaile, Stefanie and Leugering, Günter and Stingl, Michael}, booktitle = {Proceedings of the 23rd IFIP TC 7 Conference on System Modelling and Optimization}, date = {2007-07-23/2007-07-27}, faupublication = {yes}, month = {Jan}, pages = {239-250}, peerreviewed = {unknown}, publisher = {Springer Verlag}, title = {{Free} material optimization for plates and shells}, venue = {Cracow}, volume = {312}, year = {2009} } @article{faucris.117640424, abstract = {Free material design deals with the question of finding the lightest structure subject to one or more given loads when both the distribution of material and the material itself can be freely varied. We additionally consider constraints on local stresses in the optimal structure. We discuss the choice of formulation of the problem and the stress constraints. The chosen formulation leads to a mathematical program with matrix inequality constraints, so-called nonlinear semidefinite program. We present an algorithm that can solve these problems. The algorithm is based on a generalized augmented Lagrangian method. A number of numerical examples demonstrate the effect of stress constraints in free material optimization.}, author = {Kocvara, Michal and Stingl, Michael}, doi = {10.1007/s00158-007-0095-5}, faupublication = {yes}, journal = {Structural and Multidisciplinary Optimization}, keywords = {topology optimization;material optimization;stress based design;nonlinear semidefinite programming}, pages = {323-335}, peerreviewed = {Yes}, title = {{Free} material optimization for stress constraints}, volume = {33}, year = {2007} } @article{faucris.124098084, abstract = {We present a compact overview of the recent development in free material optimization (FMO), a branch of structural optimization. The goal of FMO is to design the ultimately best material (its mechanical properties and distribution in space) for a given purpose. We show that the current FMO models naturally lead to linear and non-linear semidefinite programming problems (SDP); their numerical tractability is then guaranteed by recently introduced SDP algorithms.}, author = {Kocvara, Michal and Stingl, Michael and Zowe, Jochem}, doi = {10.1080/02331930701778908}, faupublication = {yes}, journal = {Optimization}, keywords = {optimization of elastic structures;material optimization;topology optimization;semidefinite programming;method of augmented Lagrangians}, pages = {79-100}, peerreviewed = {Yes}, title = {{Free} material optimization: recent progress}, volume = {57}, year = {2008} } @article{faucris.107387104, abstract = {The goal of this paper is to formulate and solve free material optimization problems with constraints on the smallest eigenfrequency of the optimal structure. A natural formulation of this problem as a linear semidefinite program turns out to be numerically intractable. As an alternative, we propose a new approach, which is based on a nonlinear semidefinite low-rank approximation of the semidefinite dual. We introduce an algorithm based on this approach and analyze its convergence properties. The article is concluded by numerical experiments proving the effectiveness of the new approach}, author = {Stingl, Michael and Kocvara, Michal and Leugering, Günter}, doi = {10.1137/080717122}, faupublication = {yes}, journal = {SIAM Journal on Optimization}, pages = {524--547}, peerreviewed = {Yes}, title = {{Free} {Material} {Optimization} with {Fundamental} {Eigenfrequency} {Constraints}}, volume = {20}, year = {2009} } @inproceedings{faucris.239916510, author = {Peukert, Wolfgang and Segets, Doris and Haderlein, Michael and Pflug, Lukas and Leugering, Günter and Gröschel, Michael}, booktitle = {7th World Congress on Particle Technology, WCPT 2014}, date = {2014-05-19/2014-05-22}, doi = {10.1016/j.proeng.2015.01.129}, faupublication = {yes}, keywords = {in situ; characterization; process design; optical properties; quantum dots}, pages = {575-581}, peerreviewed = {No}, publisher = {Elsevier Ltd}, title = {{From} in situ characterization to process control of quantum dot systems}, venue = {Bejing}, volume = {102}, year = {2015} } @incollection{faucris.121892804, abstract = {Many important topics in multiobjective optimization and decision making have been studied in this book so far. In this chapter, we wish to discuss some new trends and challenges which the field is facing. For brevity, we here concentrate on three main issues: new problem areas in which multiobjective optimization can be of use, new procedures and algorithms to make efficient and useful applications of multiobjective optimization tools and, finally, new interesting and practically usable optimality concepts. Some research has already been started and some such topics are also mentioned here to encourage further research. Some other topics are just ideas and deserve further attention in the near future. © 2008 Springer Berlin Heidelberg.}, address = {Berlin}, author = {Jahn, Johannes and Miettinen, K. and Ogryczak, W. and Deb, K. and Shimoyama, K. and Vetschera, R.}, booktitle = {Multiobjective Optimization - Interactive and Evolutionary Approaches}, doi = {10.1007/978-3-540-88908-3-16}, editor = {J. Branke, K. Deb, K. Miettinen, R. Slowinski}, faupublication = {yes}, isbn = {3540889078}, note = {UnivIS-Import:2015-04-20:Pub.2008.nat.dma.pama21.future}, pages = {435-461}, peerreviewed = {unknown}, publisher = {Springer-verlag}, series = {Lecture Notes in Computer Science}, title = {{Future} {Challenges}}, volume = {5252 LNCS}, year = {2008} } @article{faucris.119409444, abstract = {The problem of maximizing the performance in a fiber distributed data interface (FDDI) computer network is formulated as a cooperative n-player game. Solutions of this game can be obtained by solving special optimization problems. Using the models and formulas developed by Tangemann (Ref. 1) and Klehmet (Ref. 2) for the mean waiting times, the resulting optimization problems are presented and numerical results are given.}, author = {Jahn, Johannes and Häßler, S.}, faupublication = {yes}, journal = {Journal of Optimization Theory and Applications}, keywords = {Cooperative games; Timed token rotation protocols; Vector optimization}, note = {UnivIS-Import:2015-03-09:Pub.2000.nat.dma.pama21.gameth}, pages = {463-474}, peerreviewed = {Yes}, title = {{Game}-{Theoretic} {Approach} to the {Optimization} of {FDDI} {Computer} {Networks}}, volume = {106}, year = {2000} } @article{faucris.123311144, abstract = {We analyze the subcritical gas flow through fan-shaped networks of pipes, that is, through tree-shaped networks with exactly one node where more than two pipes meet. The gas flow in pipe networks is modeled by the isothermal Euler equations, a hyperbolic PDE system of balance laws. For this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval. Furthermore, we present a Lyapunov function and boundary feedback laws to stabilize a fan-shaped network around a given stationary state. © 2011 Society for Industrial and Applied Mathematics.}, author = {Gugat, Martin and Hirsch-Dick, Markus and Leugering, Günter}, doi = {10.1137/100799824}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {Classical solutions; Critical length; Fan-shaped networks; Feedback law; Gas networks; Junction; Lyapunov function; Networked hyperbolic systems; Riemann invariants}, note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.gasflo}, pages = {2101-2117}, peerreviewed = {Yes}, title = {{Gas} {Flow} in {Fan}-{Shaped} {Networks}: {Classical} {Solutions} and {Feedback} {Stabilization}}, url = {http://epubs.siam.org/sicon/resource/1/sjcodc/v49/i5/p2101{\_}s1}, volume = {49}, year = {2011} } @article{faucris.110997084, abstract = {Necessary and sufficient optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by employing the generalized contingent epiderivative and the weak contingent epiderivative of the objective set-valued map and the set-valued map defining the constraints. The known Lagrange multiplier rule and the so-called Zowe-Kurcyusz-Robinson (cf. Robinson, S.M. Stability Theory for Systems of Inequalities. II, Differentiable Nonlinear Systems. SIAM J. Numer. Anal. 1976, 13, 497-513. Zowe, J.; Kurcyusz, S. Regularity and Stability for the Mathematical Programming Problem in Banach spaces, Appl. Math. Optim 1979, 5, 49-62.) regularity condition are extended using these differentiability notions.}, author = {Jahn, Johannes and Khan, Akhtar Ali}, doi = {10.1081/NFA-120016271}, faupublication = {yes}, journal = {Numerical Functional Analysis and Optimization}, keywords = {Aubin property; Contingent cone; Generalized contingent epiderivative; Lagrange multipliers; Optimality conditions; Regularity conditions; Set-valued optimization}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.pama21.genera}, pages = {807-831}, peerreviewed = {Yes}, title = {{Generalized} contingent epiderivatives in set-valued optimization: optimality conditions}, volume = {23}, year = {2002} } @article{faucris.110298144, abstract = {Quasiconvexity for mappings is generalized in such a way that this notion gives the sufficiency of necessary optimality conditions such as multiplier rules. One can show that it is the weakest type of generalized convexity notions in the sense that this generalized quasiconvexity holds if certain multiplier rules are sufficient for optimality. It also yields the equivalence of local and global minima. The theory is applied to a multi-objective programming problem and a vector approximation problem.}, author = {Jahn, Johannes and Sachs, E.}, faupublication = {no}, journal = {SIAM Journal on Control and Optimization}, note = {UnivIS-Import:2015-03-05:Pub.1986.nat.dma.pama21.genera}, pages = {306-322}, peerreviewed = {Yes}, title = {{Generalized} {Quasiconvex} {Mappings} and {Vector} {Optimization}}, volume = {24}, year = {1986} } @article{faucris.123196084, abstract = {Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson's ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson's ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson's ratio on the underlying material's Poisson's ratio and small values of the effective Young's modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson's ratio is material-dependent and the Young's modulus (E) over tilde (cs) large. All analysed structures of this type have positive values of the Poisson's ratio and large values of (E) over tilde (cs). Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young's modulus. (C) 2016 Elsevier Ltd. All rights reserved.}, author = {Mitschke, Holger and Schury, Fabian and Mecke, Klaus and Wein, Fabian and Stingl, Michael and Schroder-Turk, Gerd E.}, doi = {10.1016/j.ijsolstr.2016.06.027}, faupublication = {yes}, journal = {International Journal of Solids and Structures}, keywords = {Cellular structures;Homogenisation;Floppy frameworks;Auxeticity;Mechanical metamaterial}, pages = {1-10}, peerreviewed = {Yes}, title = {{Geometry}: {The} leading parameter for the {Poisson}'s ratio of bending-dominated cellular solids}, volume = {100}, year = {2016} } @article{faucris.120144244, abstract = {We consider the problem of exactly controlling the states of the de St. Venant equations from a given constant state to another constant state by applying nonlinear boundary controls. During this transition the solution stays in the class of CSince several years an engineer and a mathematician offer the course "Simulation of transportation processes using Matlab" for master students of process and power engineering. This is an interdisciplinary course where the students will get an elementary introduction to numerics and coding in Matlab/Octave, will repeat the modelling of heat flow and steady Rankine processes and combine this in some Matlab scripts. This blended course already engaged the students to work independently but to meet every two weeks for discussion and get support in programming. For the two weeks between the sessions we have prepared learning modules provided in our LMS ILIAS, which the students have to prepare. This is basis for the discussion in the presence meetings. In this learning modules, e.g. the 1d heat transfer was introduced and in parallel the idea of the finite differences of first and second order. For this a loop back was done to the engineering mathematics courses 1 and 2.

All this we turned now into a pure online course, in particular the coding sessions. Some adjustments we have done, so we offered a weekly question hour. The main headline about all is: Getting the students in to action.

At the end we have to state, that this year the students were more active and discussed the models much more deeply then before.

This course is held together with Micheal Wensing (Institute of Engineering Thermodynamics).

All this we turned now into a pure online course, in particular the coding sessions. Some adjustments we have done, so we offered a weekly question hour. The main headline about all is: Getting the students in to action.

At the end we have to state, that this year the students were more active and discussed the models much more deeply then before.

This course is held together with Micheal Wensing (Institute of Engineering Thermodynamics).

}, author = {Coclite, Giuseppe Maria and De Nitti, Nicola and Keimer, Alexander and Pflug, Lukas and Zuazua Iriondo, Enrique}, doi = {10.1088/1361-6544/acf01d}, faupublication = {yes}, journal = {Nonlinearity}, keywords = {Nonlocal conservation laws; nonlocal flux; Burgers’ equation; approximation of local conservation laws; N-waves; source-type solutions; entropy solutions}, peerreviewed = {Yes}, title = {{Long}-time convergence of a nonlocal {Burgers}' equation towards the local {N}-wave}, url = {https://iopscience.iop.org/article/10.1088/1361-6544/acf01d}, year = {2023} } @incollection{faucris.107023664, address = {München}, author = {Jahn, Johannes and Dupre, R. and Huckert, K.}, booktitle = {Ausgewählte Operations Research Software in FORTRAN}, editor = {H. Späth}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1979.nat.dma.pama21.lsungl}, pages = {9-29}, peerreviewed = {unknown}, publisher = {Oldenbourg}, title = {{Lösung} linearer {Vektormaximumprobleme} durch das {STEM}-{Verfahren}}, year = {1979} } @incollection{faucris.118332544, address = {München}, author = {Jahn, Johannes}, booktitle = {Ausgewählte Operations Research Software in FORTRAN}, editor = {H. Späth}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1979.nat.dma.pama21.lsungn}, pages = {30-50}, peerreviewed = {unknown}, publisher = {Oldenbourg}, title = {{Lösung} nichtlinearer {Optimierungsprobleme} mit {Nebenbedingungen}}, year = {1979} } @article{faucris.111517164, abstract = {We study problems of boundary controllability with minimal L -norm (p ∈ [2, ∞]) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions. The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the L-norm of the controls. We give necessary and sufficient conditions for the solvability of this problem. We show as follows how this infinite-dimensional optimization problem can be transformed into a problem which is much simpler: The feasible set of the transformed problem is described by a finite number of simple pointwise equality constraints for the control function in the Dirichlet case while, in the Neumann case, an additional integral equality constraint appears. We provide explicit complete solutions of the problems for all p ∈[2, ∞] in the Dirichlet case and solutions for some typical examples in the Neumann case. © 2005 Society for Industrial and Applied Mathematics.}, author = {Gugat, Martin and Leugering, Günter and Sklyar, Gregori}, doi = {10.1137/S0363012903419212}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {Analytic solution; Boundary control; Controllability; Distributed parameter systems; Optimal control; Robust optimization; Sensitivity; State constraints; Test examples; Wave equation}, note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.lama1.lpopti}, pages = {49-74}, peerreviewed = {Yes}, title = {{Lp}-optimal boundary control for the wave equation,}, volume = {44}, year = {2005} } @article{faucris.124194884, abstract = {Commonly applied models to study vocal fold vibrations in combination with air flow distributions are self-sustained physical models of the larynx consisting of artificial silicone vocal folds. Choosing appropriate mechanical parameters and layer geometries for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In earlier work by Schmidt et al. [J. Acoust. Soc. Am. 129, 2168-2180 (2011)], the authors presented an approach in which material parameters of a static numerical vocal fold model were optimized to achieve an agreement of the displacement field with data retrieved from hemilarynx experiments. This method is now generalized to a fully transient setting. Moreover in addition to the material parameters, the extended approach is capable of finding optimized layer geometries. Depending on chosen material restriction, significant modifications of the reference geometry are predicted. The additional flexibility in the design space leads to a significantly more realistic deformation behavior. At the same time, the predicted biomechanical and geometrical results are still feasible for manufacturing physical vocal fold models consisting of several silicone layers. As a consequence, the proposed combined experimental and numerical method is suited to guide the construction of physical vocal fold models. (C) 2013 Acoustical Society of America.}, author = {Schmidt, Bastian and Leugering, Günter and Stingl, Michael and Hüttner, Björn and Agaimy, Abbas and Döllinger, Michael}, doi = {10.1121/1.4812253}, faupublication = {yes}, journal = {Journal of the Acoustical Society of America}, pages = {1261-1270}, peerreviewed = {Yes}, title = {{Material} and shape optimization for multi-layered vocal fold models using transient loadings}, volume = {134}, year = {2013} } @article{faucris.202370051, abstract = {A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration a model is established on the basis of an appropriately parametrized material tensor. The resulting nonlinear parametrization is treated on the level of the sub-problem, for which, globally optimal solutions can be computed due to the block separability of the model. Although global optimization of non-convex design problems is generally prohibitive, a well chosen combination of analytic solutions along with standard global optimization techniques leads to a very efficient algorithm for most relevant material parametrizations. A global convergence result for the overall algorithm is established. The effectiveness of the approach in terms of both computation time and solution quality is demonstrated by numerical examples, including the optimal design of cloaking layers for a nano-particle and the identification of multiple materials with different optical properties in a matrix.}, author = {Semmler, Johannes and Pflug, Lukas and Stingl, Michael}, doi = {10.1137/17M1127569}, faupublication = {yes}, journal = {SIAM Journal on Scientific Computing}, keywords = {Discrete optimization; Global optimization; Electromagnetic scattering; Inverse problems; Helmholtz equation; Optical properties; Material optimization; Sequential programming}, pages = {B85-B109}, peerreviewed = {Yes}, title = {{Material} optimization in transverse electromagnetic scattering applications}, volume = {40}, year = {2018} } @article{faucris.117640644, abstract = {Today, the prevention and treatment of voice disorders is an ever-increasing health concern. Since many occupations rely on verbal communication, vocal health is necessary just to maintain one's livelihood. Commonly applied models to study vocal fold vibrations and air flow distributions are self sustained physical models of the larynx composed of artificial silicone vocal folds. Choosing appropriate mechanical parameters for these vocal fold models while considering simplifications due to manufacturing restrictions is difficult but crucial for achieving realistic behavior. In the present work, a combination of experimental and numerical approaches to compute material parameters for synthetic vocal fold models is presented. The material parameters are derived from deformation behaviors of excised human larynges. The resulting deformations are used as reference displacements for a tracking functional to be optimized. Material optimization was applied to three-dimensional vocal fold models based on isotropic and transverse-isotropic material laws, considering both a layered model with homogeneous material properties on each layer and an inhomogeneous model. The best results exhibited a transversal-isotropic inhomogeneous (i.e., not producible) model. For the homogeneous model (three layers), the transversal-isotropic material parameters were also computed for each layer yielding deformations similar to the measured human vocal fold deformations. (C) 2011 Acoustical Society of America. [DOI:10.1121/1.3543988]}, author = {Schmidt, Bastian and Stingl, Michael and Leugering, Günter and Berry, David A. and Döllinger, Michael}, doi = {10.1121/1.3543988}, faupublication = {yes}, journal = {Journal of the Acoustical Society of America}, pages = {2168-2180}, peerreviewed = {Yes}, title = {{Material} parameter computation for multi-layered vocal fold models}, volume = {129}, year = {2011} } @incollection{faucris.119529784, address = {Berlin}, author = {Jahn, Johannes}, booktitle = {Essays and Surveys on Multiple Criteria Decision Making}, editor = {P. Hansen}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1983.nat.dma.pama21.mathem}, pages = {177-186}, peerreviewed = {unknown}, publisher = {Springer}, series = {Lecture Notes in Economics and Mathematical Systems}, title = {{Mathematical} {Applications} of {MCDM}: {Vector} {Approximation} and {Cooperative} {Differential} {Games}}, volume = {209}, year = {1983} } @book{faucris.115716084, abstract = {Water supply- and drainage systems and mixed water channel systems are networks whose high dynamic is determined and/or affected by consumer habits on drinking water on the one hand and by climate conditions, in particular rainfall, on the other hand. According to their size, water networks consist of hundreds or thousands of system elements. Moreover, different types of decisions (continuous and discrete) have to be taken in the water management. The networks have to be optimized in terms of topology and operation by targeting a variety of criteria. Criteria may for example be economic, social or ecological ones and may compete with each other. The development of complex model systems and their use for deriving optimal decisions in water management is taking place at a rapid pace. Simulation and optimization methods originating in Operations Research have been used for several decades; usually with very limited direct cooperation with applied mathematics. The research presented here aims at bridging this gap, thereby opening up space for synergies and innovation. It is directly applicable for relevant practical problems and has been carried out in cooperation with utility and dumping companies, infrastructure providers and planning offices. A close and direct connection to the practice of water management has been established by involving application-oriented know-how from the field of civil engineering. On the mathematical side all necessary disciplines were involved, including mixed-integer optimization, multi-objective and facility location optimization, numerics for cross-linked dynamic transportation systems and optimization as well as control of hybrid systems. Most of the presented research has been supported by the joint project "Discret continuous optimization of dynamic water systems" of the federal ministry of education and research (BMBF).}, author = {Martin, Alexander and Klamroth, Kathrin and Lang, Jens and Leugering, Günter and Morsi, Antonio and Oberlack, Martin and Ostrowski, Manfred and Rosen, Roland}, faupublication = {yes}, peerreviewed = {Yes}, publisher = {Birkhäuser}, series = {International Series of Numerical Mathematics}, title = {{Mathematical} {Optimization} of {Water} {Networks}}, volume = {162}, year = {2012} } @book{faucris.108699404, address = {Frankfurt}, author = {Jahn, Johannes}, faupublication = {no}, note = {UnivIS-Import:2015-04-02:Pub.1986.nat.dma.pama21.mathem}, pages = {310}, publisher = {Peter Lang}, title = {{Mathematical} {Vector} {Optimization} in {Partially} {Ordered} {Linear} {Spaces}}, year = {1986} } @inproceedings{faucris.244448530, abstract = {Das Sommersemester 2020 hat eine neue Notwendigkeit digitaler Infrastruktur inder universitären Lehre gezeigt. In diesem Beitrag wird über den Übergang voneinem Präsenzunterricht mit Übungen und Korrektur von Hausaufgaben zu einerOnlinelehre mit Präsenz berichtet. Zentraler "Backbone" waren die Elemente, dieILIAS in Kursen zur Verfügung stellt, wie Lernmodule, Sitzungen, Gestaltung derSeiten. Zentraler Punkt für den Austausch waren das Übungsobjekt undLive-Votings als eines der wichtigen Elemente für die Interaktion und Aktivierung inden Online-Sitzungen. Die Auswertung der Live-Votings wurde anschließenddokumentiert und der Stoff gemeinsam weiterentwickelt. Somit wurde versucht,die Vorteile der Präsenzlehre in den virtuellen Raum mitzunehmen. Um einblended Learning zu unterstützen, wurde das Selbststudium gefordert undgefördert. Zudem werden Umfragen unter den Studierenden vorgestellt, die überdie Schwierigkeiten und Wünsche in Präsenz- und Onlinelehre Auskunft gebe}, author = {Rathmann, Wigand}, booktitle = {19. International ILIAS Conference}, date = {2020-09-10}, faupublication = {yes}, peerreviewed = {No}, title = {{Mathematik} – {Präsenzlehre} online}, url = {https://docu.ilias.de/goto{\_}docu{\_}file{\_}9239{\_}download.html}, venue = {Online}, year = {2020} } @inproceedings{faucris.106458924, author = {Rathmann, Wigand}, booktitle = {1. Tag der Lehre}, date = {2015-12-11}, faupublication = {yes}, peerreviewed = {No}, title = {{Mathematische} {Fragestellungen} online realisieren ({Vortrag} beim 1. {Tag} der {Lehre} an der {FAU})}, url = {https://youtu.be/GEvyM2vhm{\_}E?iframe=true}, venue = {FAU}, year = {2015} } @article{faucris.117696964, author = {Domschke, Pia and Groß, Martin and Hante, Falk and Hiller, Benjamin and Schewe, Lars and Schmidt, Martin}, faupublication = {yes}, journal = {Gas und Wasserfach, Gas, Erdgas}, pages = {880-885}, peerreviewed = {No}, title = {{Mathematische} {Modellierung}, {Simulation} und {Optimierung} von {Gastransportnetzwerken}}, url = {https://www.di-verlag.de/de/Zeitschriften/gwf-Gas-Erdgas/2015/11/Mathematische-Modellierung-Simulation-und-Optimierung-von-Gastransportnetzwerken}, volume = {156}, year = {2015} } @article{faucris.107409984, abstract = {We consider optimal control problems for linear degenerate elliptic equations with mixed boundary conditions. In particular, we take the matrix-valued coeffcients A(x) of such systems as controls in L1(;RN(N+1) 2 ). One of the important features of the admissible controls is the fact that eigenvalues of the coeffcient matrices may vanish in Equations of this type may exhibit non-uniqueness of weak solutions. Using the concept of convergence in variable spaces and following the direct method in the Calculus of variations, we establish the solvability of this optimal control problem in the class of weak admissible solutions. © European Mathematical Society.}, author = {Kogut, Peter I. and Leugering, Günter}, doi = {10.4171/ZAA/1493}, faupublication = {yes}, journal = {Zeitschrift für Analysis und ihre Anwendungen}, keywords = {Degenerate elliptic equations;control in coefficients;weighted Sobolev spaces;Lavrentieff phenomenon;direct method in the Calculus of Variations}, month = {Jan}, pages = {433-456}, peerreviewed = {Yes}, title = {{Matrix}-{Valued} {L1}-{Optimal} {Controls} in the {Coefficients} of linear elliptic problems}, volume = {32}, year = {2013} } @article{faucris.117641744, abstract = {We present a thorough investigation of the mechanical behaviour of a non-stochastic cellular auxetic structure. A combination of experimental and numerical methods is used to gain a deeper understanding of the mechanical behaviour and its dependence on the geometric properties of the cellular structure. The experimental samples are built from Ti-6Al-4V using selective electron beam melting, an additive manufacturing process giving the possibility to vary the geometry of the structure in a highly controlled manner. The use of finite element simulations and mathematical homogenisation allows us also to investigate off-axis properties of the cellular material. This leads to a more comprehensive understanding of the mechanical behaviour of the auxetics. Ultimately, the gained knowledge can be used to tailor auxetic materials to specific applications.}, author = {Schwerdtfeger, Jan and Schury, Fabian and Stingl, Michael and Wein, Fabian and Singer, Robert and Körner, Carolin}, doi = {10.1002/pssb.201084211}, faupublication = {yes}, journal = {physica status solidi (b)}, keywords = {auxetics;cellular materials;electron beam melting;finite element method;metals}, pages = {1347-1352}, peerreviewed = {Yes}, title = {{Mechanical} characterisation of a periodic auxetic structure produced by {SEBM}}, volume = {249}, year = {2012} } @article{faucris.106725564, abstract = {

Typically, exact information of the whole subdifferential is not available for intrinsically nonsmooth objective functions such as for marginal functions. Therefore, the semismoothness of the objective function cannot be proved or is even violated. In particular, in these cases standard nonsmooth methods cannot be used. In this paper, we propose a new approach to develop a converging descent method for this class of nonsmooth functions. This approach is based on continuous outer subdifferentials introduced by us. Further, we introduce on this basis a conceptual optimization algorithm and prove its global convergence. This leads to a constructive approach enabling us to create a converging descentmethod. Within the algorithmic framework, neither semismoothness nor calculation of exact subgradients are required. This is in contrast to other approaches which are usually based on the assumption of semismoothness of the

objective function.

},
author = {Knossalla, Martin},
doi = {10.1080/02331934.2018.1426579},
faupublication = {yes},
journal = {Optimization},
keywords = {Mathematical programming; nonsmooth optimization; parametric optimization; variational analysis and optimization},
month = {Jan},
pages = {1-21},
peerreviewed = {Yes},
title = {{Minimization} of marginal functions in mathematical programming based on continuous outer subdifferentials},
year = {2018}
}
@article{faucris.120013784,
abstract = {We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.},
author = {Gugat, Martin and Leugering, Günter and Martin, Alexander and Schmidt, Martin and Sirvent, Mathias and Wintergerst, David},
doi = {10.1007/s10589-017-9970-1},
faupublication = {yes},
journal = {Computational Optimization and Applications},
keywords = {Mixed-integer optimal control, Instantaneous control, Partial differential equations on graphs, Gas networks, Mixed-integer linear optimization.},
pages = {267-294},
peerreviewed = {Yes},
title = {{MIP}-based instantaneous control of mixed-integer {PDE}-constrained gas transport problems},
volume = {70},
year = {2018}
}
@misc{faucris.115699584,
author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio},
faupublication = {yes},
peerreviewed = {automatic},
title = {{Mixed} {Integer} {Linear} {Models} for the {Optimization} of {Dynamical} {Transport} {Networks}},
year = {2010}
}
@article{faucris.124196424,
abstract = {We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.},
author = {Geißler, Björn and Kolb, Oliver and Lang, Jens and Leugering, Günter and Martin, Alexander and Morsi, Antonio},
doi = {10.1007/s00186-011-0354-5},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
keywords = {Mixed integer linear programming;Piecewise linear approximation;Gas network optimization;Water network optimization},
pages = {339-362},
peerreviewed = {Yes},
title = {{Mixed} integer linear models for the optimization of dynamical transport networks},
volume = {73},
year = {2011}
}
@article{faucris.123264724,
abstract = {We consider hot forming processes, in which a metal solid body is deformed by several rolls in order to obtain a desired final shape. To minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible, we formulate an optimal control problem where we use the trajectories of the rolls as control functions. The deformation of the solid body is described through the basic equations of nonlinear continuum mechanics, which are here coupled with an elasto-viscoplastic material model based on a multiplicative split of the deformation gradient. We assume that the deformations of the rolls can be neglected, thus we add unilateral frictional contact boundary conditions, resulting in an evolutionary quasi-variational inclusion. The associated control-to-observation map is non-differentiable due to changes of state between elastic and plastic material behavior, contact and separation and stick and slip motion, yet we still want to apply gradient-based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist. To resolve this issue, we first regularize all non-differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information. Finally, we formulate a suitable algorithm and discuss numerical results for a real-world example to illustrate its capability. (C) 2017 Elsevier B.V. All rights reserved.},
author = {Werner, Stefan and Stingl, Michael and Leugering, Günter},
doi = {10.1016/j.cma.2017.03.006},
faupublication = {yes},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {Optimal control; Regularization; Sensitivity analysis; Nonlinear continuum mechanics; Frictional contact; Elasto-viscoplasticity},
pages = {442-471},
peerreviewed = {Yes},
title = {{Model}-based control of dynamic frictional contact problems using the example of hot rolling},
volume = {319},
year = {2017}
}
@article{faucris.117817084,
abstract = {Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphat},
author = {Elbinger, Tobias and Gahn, Markus and Hante, Falk and Voll, Lars and Leugering, Günter and Knabner, Peter and Neuss-Radu, Maria},
doi = {10.3389/fbioe.2016.00013},
faupublication = {yes},
journal = {Frontiers in Bioengineering and Biotechnology},
peerreviewed = {Yes},
title = {{Model}-{Based} {Design} of {Biochemical} {Microreactors}},
url = {https://www1.am.uni-erlangen.de/research/publications/Jahr{\_}2016/2016{\_}ElbingerGahnNeusRaduHanteVollLeugering{\_}ModelBasedDesignOfBioMicroReact},
year = {2016}
}
@article{faucris.237823264,
abstract = {In order to obtain high-quality particulate products with tailored properties, process conditions and their evolution in time must be chosen appropriately. Although the efficiency of these products depends on their dispersity in several dimensions, in established processes the particle size is usually the decisive variable to adjust. As part of the synthesis of these products, feedback modules are often incorporated so that a time-dependent ratio of the obtained product can flow back into the system. Moreover, the synthesis should be an energy- and resource-efficient process. To provide a means of ensuring this requirement, a model- and gradient-based, numerically efficient optimization tool for particle synthesis is presented which was developed to describe population balance equations incorporating feedback terms.},
author = {Spinola, Michele and Keimer, Alexander and Segets, Doris and Leugering, Günter and Pflug, Lukas},
doi = {10.1002/ceat.201900515},
faupublication = {yes},
journal = {Chemical Engineering & Technology},
keywords = {Feedback modules; Gradient-based optimization; Population balance equation; Ripening process},
note = {CRIS-Team Scopus Importer:2020-04-28},
pages = {896-903},
peerreviewed = {Yes},
title = {{Model}-{Based} {Optimization} of {Ripening} {Processes} with {Feedback} {Modules}},
volume = {43},
year = {2020}
}
@incollection{faucris.241184099,
abstract = {We consider the processes of particle nucleation, growth, precipitation and ripening via modeling by nonlinear 1-D hyperbolic partial integro differential equations. The goal of this contribution is to provide a concise predictive forward modeling of the processes including appropriate goal functions and to establish a mathematical theory for the open-loop optimization
in this context. Beyond deriving optimality conditions in the synthesis
process, we present the application of a fully implicit method for
Ostwald ripening of ZnO quantum
dots which preserves its numeric stability even with respect to the
inherent high sensitivities and wide disparity of scales. FIMOR
represents an appropriate method that can be integrated to subordinate optimization studies which enables its future application in the context of continuous particle syntheses and microreaction technology (MRT},
author = {Gröschel, Michael and Peukert, Wolfgang and Leugering, Günter},
booktitle = {Trends in PDE Constrained Optimization},
doi = {10.1007/978-3-319-05083-6{\_}30},
editor = {Günter Leugering; Peter Benner; Sebastian Engell; Andreas Griewank; Helmut Harbrecht; Michael Hinze; Rolf Rannacher; Stefan Ulbrich},
faupublication = {yes},
keywords = {Numerical simulation; Nonlinear integro-partial differential equation; Ostwald ripening; Optimization; Particle synthesis; Particle growth},
pages = {471-486},
peerreviewed = {unknown},
publisher = {Springer},
series = {International Series of Numerical Mathematics},
title = {{Modeling}, analysis and optimization of particle growth, nucleation and ripening by the way of nonlinear hyperbolic integro-partial differential equations},
volume = {165},
year = {2014}
}
@article{faucris.112038344,
abstract = {We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system. © 2008 Springer Science+Business Media, LLC.},
author = {Hante, Falk and Leugering, Günter and Seidman, Thomas I.},
doi = {10.1007/s00245-008-9057-6},
faupublication = {yes},
journal = {Applied Mathematics and Optimization},
keywords = {Automated switching; Hybrid system; Networked system; Optimal control; Transport equation},
note = {UnivIS-Import:2015-03-09:Pub.2009.nat.dma.lama1.modeli},
pages = {275-292},
peerreviewed = {Yes},
title = {{Modeling} and {Analysis} of {Modal} {Switching} in {Networked} {Transport} {Systems}},
url = {http://www.springerlink.com/content/v31p353l09057015/},
volume = {59},
year = {2009}
}
@incollection{faucris.122683924,
abstract = {The purpose of this paper is to disduss, in a fairly heuristic way, certain aspects of modelling and controllability of flexible, multi-beam structures from the point of view of local modelling of the structure by distributed parameter systems.},
address = {Berlin, Heidelberg},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {System Modelling and Optimization - Proceedings of the 15th IFIP Conference Zurich, Switzerland, September 2–6, 1991},
doi = {10.1007/BFb0113314},
editor = {L.D. Davisson; A.G.J. MacFarlane; H. Kwakernaak; J.L. Massey; Ya Z. Tsypkin; A.J. Viterbi; Peter Kall},
faupublication = {no},
isbn = {978-3-540-47220-9},
month = {Jan},
pages = {467-480},
peerreviewed = {unknown},
publisher = {New York; Springer; 1999},
series = {Lecture Notes in Control and Information Sciences},
title = {{MODELING} {AND} {CONTROLLABILITY} {OF} {NETWORKS} {OF} {THIN} {BEAMS}},
url = {http://link.springer.com/chapter/10.1007/BFb0113314},
volume = {180},
year = {1992}
}
@article{faucris.121613404,
abstract = {The purpose of this paper is to derive junction conditions for networks of thin elastic plates and to analyse the dynamic equations of such networks. Junction conditions for networks of Kirchhoff plates and networks of Reissner-Mindlin plates are derived based on geometric considerations of the deformation at a junction. It is proved that the dynamic system which describes the Reissner-Mindlin network is well-posed is an appropriate energy space. It is further established that the Kirchhoff network is obtained in the limit of the Reissner-Mindlin network as the shear moduli go to infinity.},
author = {Langnese, John E. and Leugering, Günter},
doi = {10.1002/mma.1670160602},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
pages = {379-407},
peerreviewed = {Yes},
title = {{MODELING} {OF} {DYNAMIC} {NETWORKS} {OF} {THIN} {ELASTIC} {PLATES}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670160602/full},
volume = {16},
year = {1993}
}
@article{faucris.117908824,
abstract = {We derive a distributed-parameter model of a thin non-linear thermoelastic beam in three dimensions. The beam can also be initially curved and twisted. Our main task is to formulate the non-homogeneous initial, boundary and node value problem associated with the dynamics of a network of a finite number of such beams. The emphasis here is on a distributed-parameter modelling of the geometric and kinematic node conditions. The forces and couples appearing in the boundary and node conditions can then be viewed as control variables. The analysis of the resulting control systems and their controllability and stabilizability properties is the subject of [25] and of forthcoming papers.},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
doi = {10.1002/mma.1670160503},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
pages = {327-358},
peerreviewed = {Yes},
title = {{MODELING} {OF} {DYNAMIC} {NETWORKS} {OF} {THIN} {THERMOELASTIC} {BEAMS}},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670160503/full},
volume = {16},
year = {1993}
}
@incollection{faucris.122007864,
abstract = {This chapter focuses on acoustic, electromagnetic, elastic and piezo-electric wave propagation through heterogenous layers. The motivation is provided by the demand for a better understanding of meta-materials and their possible construction. We stress the analogies between the mathematical treatment of phononic, photonic and elastic meta-materials. Moreover, we treat the cloaking problem in more detail from an analytical and simulation oriented point of view. The novelty in the approach presented here is with the interlinked homogenization- and optimization procedur},
author = {Leugering, Günter and Rohan, Eduard and Seifrt, Frantiek},
booktitle = {Wave Propagation in Periodic Media},
doi = {10.2174/978160805150211001010197},
editor = {Matthias Ehrhardt},
faupublication = {yes},
note = {EAM Import::2019-03-12},
pages = {197-226},
peerreviewed = {unknown},
publisher = {Bentham Science},
series = {Progress in Computational Physics},
title = {{Modeling} of {Metamaterials} in {Wave} {Propagation}},
volume = {1},
year = {2010}
}
@incollection{faucris.240105087,
author = {Spinola, Michele and Keimer, Alexander and Segets, Doris and Pflug, Lukas and Leugering, Günter},
booktitle = {Dynamic Flowsheet Simulation of Solids Processes},
doi = {10.1007/978-3-030-45168-4},
editor = {Heinrich, Stefan},
faupublication = {yes},
isbn = {978-3-030-45167-7},
pages = {549-578},
peerreviewed = {unknown},
publisher = {Springer International Publishing},
title = {{Modeling}, {Simulation} and {Optimization} of {Process} {Chains}},
year = {2020}
}
@book{faucris.122826924,
address = {Bayreuth},
author = {Rathmann, Wigand},
faupublication = {no},
peerreviewed = {Yes},
publisher = {University of Bayreuth},
series = {Bayreuther Mathematische Schriften},
title = {{Modellierung}, {Simulation} und {Steuerung} von {Netzwerken} schwingender {Balken} mittels dynamischer {Bereichszerlegung}},
volume = {60},
year = {2000}
}
@incollection{faucris.122007644,
address = {Berlin},
author = {Gugat, Martin and Leugering, Günter and Schittkowski, Klaus and Schmidt, E. J. P. Georg},
booktitle = {Online Optimization of Large Scale Systems},
doi = {10.1007/978-3-662-04331-8{\_}16},
faupublication = {no},
isbn = {3-540-42459-8},
note = {UnivIS-Import:2015-04-20:Pub.2001.nat.dma.zentr.modell},
pages = {251-270},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Modelling}, stabilization and control of flow in networks of open channels},
year = {2001}
}
@article{faucris.107336064,
abstract = {The production of nanoscaled particulate products with exactly pre-defined characteristics is of enormous economic relevance. Although there are different particle formation routes they may all be described by one class of equations. Therefore, simulating such processes comprises the solution of nonlinear, hyperbolic integro-partial differential equations. In our project we aim to study this class of equations in order to develop efficient tools for the identification of optimal process conditions to achieve desired product properties. This objective is approached by a joint effort of the mathematics and the engineering faculty. Two model-processes are chosen for this study, namely a precipitation process and an innovative aerosol process allowing for a precise control of residence time and temperature. Since the overall problem is far too complex to be solved directly a hierarchical sequence of simplified problems has been derived which are solved consecutively. In particular, the simulation results are finally subject to comparison with experiments.},
author = {Gröschel, Michael and Leugering, Günter and Peukert, Wolfgang},
doi = {10.1007/978-3-0348-0133-1{\_}28},
faupublication = {yes},
journal = {International Series of Numerical Mathematics},
keywords = {Population balance equations; optimal control; model reduction; parameter identification},
pages = {541-559},
peerreviewed = {Yes},
title = {{Model} {Reduction}, {Structure}-property {Relations} and {Optimization} {Techniques} for the {Production} of {Nanoscale} {Particles}},
url = {http://link.springer.com/chapter/10.1007%2F978-3-0348-0133-1{\_}28},
year = {2011}
}
@article{faucris.122009624,
abstract = {We present a mathematical framework for the so-called multidisciplinary free material optimization (MDFMO) problems, a branch of structural optimization in which the full material tensor is considered as a design variable. We extend the original problem statement by a class of generic constraints depending either on the design or on the state variables. Among the examples are local stress or displacement constraints. We show the existence of optimal solutions for this generalized free material optimization (FMO) problem and discuss convergent approximation schemes based on the finite element method.},
author = {Haslinger, J. and Kocvara, Michal and Leugering, Günter and Stingl, Michael},
doi = {10.1137/090774446},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
pages = {2709},
peerreviewed = {Yes},
title = {{Multidisciplinary} {Free} {Material} {Optimization}},
volume = {70},
year = {2010}
}
@article{faucris.111527724,
author = {Jahn, Johannes and Hillermeier, C.},
faupublication = {yes},
journal = {Surveys on Mathematics for Industry},
note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.pama21.multio},
pages = {1-42},
peerreviewed = {unknown},
title = {{Multiobjective} optimization: survey of methods and industrial applications},
volume = {11},
year = {2005}
}
@article{faucris.111690964,
abstract = {This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test problems. © 2006 Springer Science + Business Media, LLC.},
author = {Jahn, Johannes},
doi = {10.1007/s10589-006-6450-4},
faupublication = {yes},
journal = {Computational Optimization and Applications},
keywords = {Global optimization; Random search; Vector optimization},
note = {UnivIS-Import:2015-03-09:Pub.2006.nat.dma.pama21.multio},
pages = {161-175},
peerreviewed = {Yes},
title = {{Multiobjective} {Search} {Algorithm} with {Subdivision} {Technique}},
volume = {35},
year = {2006}
}
@article{faucris.266498134,
abstract = {In this work, we are interested in tree-shaped networks of freely vibrating beams which are geometrically exact (GEB) - in the sense that large motions (deflections, rotations) are accounted for in addition to shearing - and linked by rigid joints. For the intrinsic GEB formulation, namely that in terms of velocities and internal forces/moments, we derive transmission conditions and show that the network is locally in time well-posed in the classical sense. Applying velocity feedback controls at the external nodes of a star-shaped network, we show by means of a quadratic Lyapunov functional and the theory developed by Bastin & Coron in [2] that the zero steady state of this network is exponentially stable for the H-1 and H-2 norms. The major obstacles to overcome in the intrinsic formulation of the GEB network, are that the governing equations are semilinar, containing a quadratic nonlinearity, and that linear lower order terms cannot be neglected.},
author = {Rodriguez, Charlotte},
doi = {10.3934/mcrf.2021002},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
note = {CRIS-Team WoS Importer:2021-11-26},
peerreviewed = {Yes},
title = {{NETWORKS} {OF} {GEOMETRICALLY} {EXACT} {BEAMS}: {WELL}-{POSEDNESS} {AND} {STABILIZATION}},
year = {2020}
}
@incollection{faucris.121574244,
address = {Berlin},
author = {Jahn, Johannes},
booktitle = {Operations Research Proceedings 1983},
editor = {H. Steckhan, W. Bühler, K.-E. Jäger, Ch. Schneeweiß, J. Schwarze},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1984.nat.dma.pama21.neuere},
pages = {511-519},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Neuere} {Entwicklungen} in der {Vektoroptimierung}},
year = {1984}
}
@article{faucris.110289344,
abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H2-Lyapunov function and hence also the H2-norm of the difference between the non-stationary and the stationary state decays exponentially with tim},
author = {Gugat, Martin and Leugering, Günter and Wang, Ke},
doi = {10.3934/mcrf.2017015},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary feedback control, feedback stabilization, exponential stability, isothermal Euler equations, second-order quasilinear equation, Lyapunov function, stationary state, non-stationary state, gas pipeline},
pages = {419 - 448},
peerreviewed = {Yes},
title = {{Neumann} boundary feedback stabilization for a nonlinear wave equation: {A} strict {H2}-{Lyapunov} function},
volume = {7},
year = {2017}
}
@article{faucris.107392824,
abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H-2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H-2-Lyapunov function and hence also the H-2-norm of the difference between the non-stationary and the stationary state decays exponentially with time.},
author = {Leugering, Günter and Gugat, Martin and Wang, Ke},
doi = {10.3934/mcrf.2017015},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary feedback control;feedback stabilization;exponential stability;isothermal Euler equations;second-order quasilinear equation;Lyapunov function;stationary state;non-stationary state;gas pipeline},
pages = {419-448},
peerreviewed = {Yes},
title = {{NEUMANN} {BOUNDARY} {FEEDBACK} {STABILIZATION} {FOR} {A} {NONLINEAR} {WAVE} {EQUATION}: {A} {STRICT} {H}-2-{LYAPUNOV} {FUNCTION}},
volume = {7},
year = {2017}
}
@article{faucris.112460964,
abstract = {In this paper we study a set optimization problem (SOP), i. e. we minimize a set-valued objective map F, which takes values on a real linear space Y equipped with a pre-order induced by a convex cone K. We introduce new order relations on the power set P(Y) of Y (or on a subset of it), which are more suitable from a practical point of view than the often used minimizers in set optimization. Next, we propose a simple two-steps unifying approach to studying (SOP) w. r. t. various order relations. Firstly, we extend in a unified scheme some basic concepts of vector optimization, which are defined on the space Y up to an arbitrary nonempty pre-ordered set(Q) without any topological or linear structure. Namely, we define the following concepts w. r. t. the pre-order : minimal elements, semicompactness, completeness, domination property of a subset of Q, and semicontinuity of a set-valued map with values in Q in a topological setting. Secondly, we establish existence results for optimal solutions of (SOP), when F takes values on(Q) from which one can easily derive similar results for the case, when F takes values on P(Y) equipped with various order relations. © 2010 Springer Science+Business Media, LLC.},
author = {Jahn, Johannes and Ha, T.X.D.},
doi = {10.1007/s10957-010-9752-8},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Existence results; Order relations; Set optimization},
note = {UnivIS-Import:2015-03-09:Pub.2011.nat.dma.pama21.neword},
pages = {209-236},
peerreviewed = {Yes},
title = {{New} {Order} {Relations} in {Set} {Optimization}},
volume = {148},
year = {2011}
}
@article{faucris.119850544,
author = {Hante, Falk and Mommer, Mario and Potschka, Andreas},
doi = {10.1137/140967969},
faupublication = {yes},
journal = {SIAM Journal on Numerical Analysis},
pages = {2206-2225},
peerreviewed = {Yes},
title = {{Newton}-{Picard} preconditioners for time-periodic parabolic optimal control problems},
volume = {53},
year = {2015}
}
@book{faucris.119359504,
author = {Pratelli, Aldo and Leugering, Günter},
doi = {10.1007/978-3-319-17563-8},
faupublication = {yes},
isbn = {978-3-319-17563-8},
month = {Jan},
pages = {VII-VIII},
peerreviewed = {unknown},
publisher = {Springer International Publishing},
series = {International Series of Numerical Mathematics},
title = {{New} {Trends} in {Shape} {Optimization}},
url = {http://link.springer.com/book/10.1007/978-3-319-17563-8},
volume = {166},
year = {2015}
}
@incollection{faucris.116884504,
abstract = {We consider a network where a dynamical process governed by hyperbolic conservation laws takes place. At the vertices, the conservation laws are coupled by algebraic node conditions. The system is also controlled at the vertices through these conditions. To solve problems of optimal control for such a system, an adjoint sensitivity calculus is useful since it allows the efficient evaluation of the gradient of the objective function. We present such a calculus in the framework of classical solutions.},
address = {Boca Raton},
author = {Gugat, Martin},
booktitle = {Control and Boundary Analysis},
editor = {John Cagnol and Jean-Paul Zolesio},
faupublication = {yes},
keywords = {Sensitivy calculus, adkoint system},
note = {UnivIS-Import:2015-04-20:Pub.2005.nat.dma.lama1.nodalc},
pages = {201-214},
peerreviewed = {Yes},
publisher = {Chapman & Hall/CRC Press},
series = {Pure and Applied Mathematics},
title = {{Nodal} {Control} of {Conservation} {Laws} on {Networks}},
volume = {240},
year = {2005}
}
@article{faucris.262677645,
abstract = {In this work, we consider networks of so-called geometrically exact beams, namely, shearable beams that may undergo large motions. The corresponding mathematical model, commonly written in terms of displacements and rotations expressed in a fixed basis (Geometrically Exact Beam model, or GEB), has a quasilinear governing system. However, the model may also be written in terms of intrinsic variables expressed in a moving basis attached to the beam (Intrinsic GEB model, or IGEB) and while the number of equations is then doubled, the latter model has the advantage of being of first-order, hyperbolic and only semilinear. First, for any network, we show the existence and uniqueness of semi-global in time classical solutions to the IGEB model (i.e., for arbitrarily large time intervals, provided that the data are small enough). Then, for a specific network containing a cycle, we address the problem of local exact controllability of nodal profiles for the IGEB model – we steer the solution to satisfy given profiles at one of the multiple nodes by means of controls applied at the simple nodes – by using the constructive method of Zhuang, Leugering and Li (2018) [52]. Afterwards, for any network, we show that the existence of a unique classical solution to the IGEB network implies the same for the corresponding GEB network, by using that these two models are related by a nonlinear transformation. In particular, this allows us to give corresponding existence, uniqueness and controllability results for the GEB network.},
author = {Leugering, Günter and Rodriguez, Charlotte and Wang, Yue},
doi = {10.1016/j.matpur.2021.07.007},
faupublication = {yes},
journal = {Journal De Mathematiques Pures Et Appliquees},
keywords = {Geometrically exact beam; Networks; Nodal profile controllability; Well-posedness},
note = {CRIS-Team Scopus Importer:2021-08-13},
peerreviewed = {Yes},
title = {{Nodal} profile control for networks of geometrically exact beams},
year = {2021}
}
@inproceedings{faucris.234141280,
author = {Keimer, Alexander and Pflug, Lukas and Spinola, Michele},
booktitle = {10},
date = {2018-06-25/2018-06-29},
editor = {AIMS Series on Applied Mathematics},
faupublication = {yes},
pages = {475-482},
peerreviewed = {unknown},
title = {{Nonlocal} balance laws - results on existence, uniqueness and regularity},
url = {https://www.aimsciences.org/book/AM/volume/Volume 10},
venue = {Pennsylvania State University, University Park (USA)},
year = {2020}
}
@article{faucris.228833204,
abstract = {This study considers nonlocal conservation laws in which the velocity depends nonlocally on the solution not in real time but in a time-delayed manner. Nonlocal refers to the fact that the velocity of the conservation law depends on the solution integrated over a specific area in space. In every model modelling human’s behavior a time delay as reaction/response time is crucial. We distinguish a so called nonlocal classical delay model where only the velocity of the conservation law is delayed from a more realistic nonlocal delay model where also a shift backwards in space is considered. For both models we show existence and uniqueness of the solutions and study their analytical properties. We also present a direct application in traffic flow modelling. We also show that for delay approaching zero, the solutions of the considered delayed models converge to the solutions of the non-delayed models in the proper topology. Finally, a comprehensive numerical study illustrating exemplary the impacts of delay and nonlocality are presented and compared with nonlocal models without delay, as well as the corresponding local models.},
author = {Keimer, Alexander and Pflug, Lukas},
doi = {10.1007/s00030-019-0597-z},
faupublication = {yes},
journal = {Nodea-Nonlinear Differential Equations and Applications},
keywords = {Convergence for vanishing delay; Delay; Existence; LWR PDE with delay; Nonlocal balance laws; Nonlocal conservation laws; Traffic flow modelling with delay; Uniqueness},
note = {CRIS-Team Scopus Importer:2019-11-08},
peerreviewed = {Yes},
title = {{Nonlocal} conservation laws with time delay},
volume = {26},
year = {2019}
}
@article{faucris.216448317,
abstract = {We consider a nonlocal conservation law on a bounded spatial domain and show existence and uniqueness of weak solutions for nonnegative flux function and left-hand-side boundary datum. The nonlocal term is located in the flux function of the conservation law, averaging the solution by means of an integral at every spatial coordinate and every time, forward in space. This necessitates the prescription of a kind of right-hand-side boundary datum, the external impact on the outflow. The uniqueness of the weak solution follows without prescribing an entropy condition. Allowing the velocity to become zero (also dependent on the nonlocal impact) offers more realistic modeling and significantly higher applicability. The model can thus be applied to traffic flow, as suggested for unbounded domains in [S. Blandin and P. Goatin, Numer. Math., 132 (2016), pp. 217-241], [P. Goatin and S. Scialanga, Netw. Hetereog. Media, 11 (2016), pp. 107-121]. It possesses finite acceleration and can be interpreted as a nonlocal approximation of the famous "local" Lighthill-Whitham-Richards model [M. Lighthill and G. Whitham, Proc. Roy. Soc. London Ser. A, 229 (1955), pp. 281-316], [P. I. Richards, Oper. Res., 4 (1956), pp. 42-51]. Several numerical examples are presented and discussed also with respect to the reasonableness of the required assumptions and the model itself.},
author = {Pflug, Lukas and Spinola, Michele and Keimer, Alexander},
doi = {10.1137/18M119817X},
faupublication = {yes},
journal = {SIAM Journal on Mathematical Analysis},
keywords = {first order macroscopic traffic flow model with finite acceleration;nonlocal conservation law;initial boundary value problem;method of characteristics;fixed-point problem},
month = {Jan},
pages = {6271-6306},
peerreviewed = {Yes},
title = {{NONLOCAL} {SCALAR} {CONSERVATION} {LAWS} {ON} {BOUNDED} {DOMAINS} {AND} {APPLICATIONS} {IN} {TRAFFIC} {FLOW}},
volume = {50},
year = {2018}
}
@article{faucris.246705191,
abstract = {In this contribution, we study the existence and uniqueness of nonlocal transport equations. The term "nonlocal" refers to the fact that the flux function's derivative will be integrated over a neighborhood of the corresponding space-time coordinate. We will demonstrate existence and uniqueness of weak solutions for TV ∩ L∞ initial datum and provide stability estimates. Moreover, we investigate the convergence of the nonlocal transport equation to the corresponding local conservation law when the nonlocal reach tends to zero. For quadratic flux functions (including Burgers' equation and the Lighthill-Whitham-Richards traffic flow model), we establish convergence to a weak solution of the local conservation law for "symmetric" nonlocal terms. For specific quasi-convex and quasiconcave initial datum we even obtain convergence to the local entropy solution. We demonstrate that for "nonsymmetric" nonlocal approximations the solution cannot converge to the entropy solution or even a weak solution. We conclude with additional numerical examples showing that convergence appears to hold for more general initial datum.},
author = {Coron, Jean Michel and Keimer, Alexander and Pflug, Lukas},
doi = {10.1137/20M1331652},
faupublication = {yes},
journal = {SIAM Journal on Mathematical Analysis},
keywords = {convergence nonlocal to local; entropy solution; nonlocal advection equation; nonlocal balance laws; nonlocal conservation laws; nonlocal transport equations},
note = {CRIS-Team Scopus Importer:2020-12-11},
pages = {5500-5532},
peerreviewed = {Yes},
title = {{Nonlocal} {Transport} {Equations}-{Existence} and {Uniqueness} of {Solutions} and {Relation} to the {Corresponding} {Conservation} {Laws}},
volume = {52},
year = {2020}
}
@incollection{faucris.289687828,
abstract = {We consider nonoverlapping domain decomposition methods for p-type ordinary and partial differential equations and corresponding optimal control problems on metric graphs. As an exemplary context, we choose a doubly nonlinear p-parabolic model with [Formula presented] which can be retrieved from the one-dimensional Euler system and that has come to be known as friction dominated flow in gas pipe networks. We introduce an optimal control problem for such systems on a metric graph, where the pipes are represented by the edges. We then apply the rolling horizon approach and obtain a sequence of static optimal control problems of p-type. The main interest of this survey article is to describe and utilize nonoverlapping domain decomposition procedures for such optimal control problems in the context of virtual controls which lead to a decomposition of the entire optimality system such that the decomposed system is itself the optimality system of an optimal control problem. This transfers the parallel iterative domain decomposition method into a sequence of parallel optimal control problems. We depart from the classical domain decomposition methods described by P.L. Lions (1990) and J.L. Lions and O. Pironneau (1998, 1999, 2000) and extend those to problems on metric graphs. We provide some numerical simulations.},
author = {Leugering, Günter},
booktitle = {Handbook of Numerical Analysis},
doi = {10.1016/bs.hna.2022.11.002},
editor = {Emmanuel Trélat, Enrique Zuazua},
faupublication = {yes},
keywords = {Domain decomposition; Instantaneous control; Optimal control; Optimality system; p-Laplace problem on a graph; p-parabolic problems; Pdes on graphs},
month = {Jan},
note = {CRIS-Team Scopus Importer:2023-02-24},
pages = {217-260},
peerreviewed = {unknown},
publisher = {Elsevier B.V.},
title = {{Nonoverlapping} domain decomposition and virtual controls for optimal control problems of p-type on metric graphs},
volume = {24},
year = {2023}
}
@article{faucris.320535669,
abstract = {We consider a non-overlapping domain decomposition method for optimal control problems of the tracking type governed by time-fractional diffusion equations in one space dimension, where the fractional time derivative is considered in the Caputo sense. We concentrate on a transmission problem defined on two adjacent intervals, where at the interface we introduce an iterative non-overlapping domain decomposition in the spirit of P.L. Lions for the corresponding first-order optimality system, such that the optimality system corresponding to the optimal control problem on the entire domain is iteratively decomposed into two systems on the respective sub-domains; this approach can be framed as first optimize, then decompose. We show that the iteration involving the states and adjoint states converges in the appropriate spaces. Moreover, we show that the decomposed systems on the sub-domain can in turn be interpreted as optimality systems of so-called virtual control problems on the sub-domains. Using this property, we are able to solve the original optimal control problem by an iterative solution of optimal control problems on the sub-domains. This approach can be framed as first decompose, then optimize. We provide a mathematical analysis of the problems as well as a numerical finite difference discretization using the L1-method with respect to the Caputo derivative, along with two examples in order to verify the method.},
author = {Leugering, Günter and Mehandiratta, Vaibhav and Mehra, Mani},
doi = {10.3390/fractalfract8030129},
faupublication = {yes},
journal = {Fractal and Fractional},
keywords = {Caputo fractional derivative; domain decomposition; optimal control; time-fractional diffusion equation},
note = {CRIS-Team Scopus Importer:2024-04-05},
peerreviewed = {Yes},
title = {{Non}-{Overlapping} {Domain} {Decomposition} for {1D} {Optimal} {Control} {Problems} {Governed} by {Time}-{Fractional} {Diffusion} {Equations} on {Coupled} {Domains}: {Optimality} {System} and {Virtual} {Controls}},
volume = {8},
year = {2024}
}
@article{faucris.119464224,
abstract = {We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs - ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.},
author = {Leugering, Günter and Martin, Alexander and Schmidt, Martin and Sirvent, Mathias},
faupublication = {yes},
journal = {Control and Cybernetics},
keywords = {Optimal control; Gas networks; Euler's equation; Semilinear PDE; Nonoverlapping domain decomposition},
pages = {191-225},
peerreviewed = {Yes},
title = {{Nonoverlapping} {Domain} {Decomposition} for {Optimal} {Control} {Problems} governed by {Semilinear} {Models} for {Gas} {Flow} in {Networks}},
volume = {46},
year = {2017}
}
@article{faucris.113909884,
abstract = {We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control at the other end. We give an explicit representation of the
A vibrating plate is here taken to satisfy the model equation:*u*_{tt} + Δ^{2}u = 0 (where*Δ*^{2}u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:*u*_{v} = 0 and*(Δu)*_{v} = ϕ = control. Thus, the state is the pair [*u, u*_{t}] and controllability means existence of*ϕ* on Σ:= (0,*T*)×*∂Ω* transfering ‘any’*[u, u*_{t}]_{0} to ‘any’*[u, u*_{t}]_{T}. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For large*T* one has such controllability with*∥ϕ∥ = O(T*^{−1/2}). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:*u*_{tt} = Δu) with log*∥ϕ∥ = O(T*^{−1}) as*T*→0. Some related results on minimum time control are also included.

}, author = {Leugering, Günter and Krabs, W. and Seidman, Thomas I.}, doi = {10.1007/BF01442208}, faupublication = {no}, journal = {Applied Mathematics and Optimization}, pages = {205-229}, peerreviewed = {Yes}, title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {A} {VIBRATING} {PLATE}}, url = {http://link.springer.com/article/10.1007/BF01442208}, volume = {13}, year = {1985} } @article{faucris.117909924, abstract = {This paper is concerned with boundary control of one-dimensional vibrating media whose motion is governed by a wave equation with a 2

For vibrating strings also, null-controllability by L(p)-controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.},
author = {Krabs, W. and Leugering, Günter},
doi = {10.1002/mma.1670170202},
faupublication = {no},
journal = {Mathematical Methods in the Applied Sciences},
pages = {77-93},
peerreviewed = {Yes},
title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {ONE}-{DIMENSIONAL} {VIBRATING} {SYSTEMS} {BY} {W}(0)1,{P}-{CONTROLS} {FOR} p∈[2, ∞]},
url = {http://onlinelibrary.wiley.com/doi/10.1002/mma.1670170202/abstract},
volume = {17},
year = {1994}
}
@article{faucris.117910144,
abstract = {It is shown that a general isotropic viscoelastic solid with non vanishing Newtonian viscosity is never exactly controllable using L_{2}-boundary controls. For some models it is known that even spectral controllability does not hold. Here we show, thereby extending results obtained in Leugering and Schmidt [10], that the general model is approximatively controllable under some reasonable assumptions.},
author = {Leugering, Günter},
doi = {10.1007/BFb0002592},
faupublication = {no},
journal = {Lecture Notes in Control and Information Sciences},
month = {Jan},
pages = {190-201},
peerreviewed = {Yes},
title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {VISCOELASTIC} {SYSTEMS} - {Proceedings} of the {IFIP} {WG} 7.2 {Working} {Conference} {Santiago} de {Compostela}, {Spain}, {July} 6–9, 1987},
url = {http://link.springer.com/chapter/10.1007/BFb0002592},
volume = {114},
year = {1989}
}
@article{faucris.117910364,
author = {Leugering, Günter},
doi = {10.1007/BFb0041994},
faupublication = {no},
journal = {Lecture Notes in Control and Information Sciences},
month = {Jan},
pages = {234-252},
peerreviewed = {Yes},
title = {{ON} {BOUNDARY} {CONTROLLABILITY} {OF} {VOLTERRA} {INTEGRODIFFERENTIAL} {EQUATIONS} {IN} {HILBERT}-{SPACES}},
url = {http://link.springer.com/chapter/10.1007/BFb0041994},
volume = {102},
year = {1987}
}
@article{faucris.264862056,
abstract = {In this paper, we study exact boundary controllability for a linear wave equation with strong and weak interior degeneration of the coefficient in the principle part of the elliptic operator. The objective is to provide a well-posedness analysis of the corresponding system and derive conditions for its controllability through boundary actions. Passing to a relaxed version of the original problem, we discuss existence and uniqueness of solutions, and using the HUM method we derive conditions on the rate of degeneracy for both exact boundary controllability and the lack thereof.},
author = {Kogut, Peter I. and Kupenko, Olga P. and Leugering, Günter},
doi = {10.1002/mma.7811},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
keywords = {boundary control; degenerate wave equation; exact controllability; existence result; weighted Sobolev spaces},
note = {CRIS-Team Scopus Importer:2021-10-08},
peerreviewed = {Yes},
title = {{On} boundary exact controllability of one-dimensional wave equations with weak and strong interior degeneration},
year = {2021}
}
@article{faucris.120846704,
abstract = {It is shown that a cantilevered beam with weak viscoelastic damping of Boltzmann-type can be uniformly stabilised by velocity feedback applied as a shearing force at the free end of the beam. Estimates for the viscoelastic energy are derived using the energy multiplier method. The energy decay is related to the decay of the relaxation modulus associated with the viscoelastic material.},
author = {Leugering, Günter},
doi = {10.1017/S0308210500024264},
faupublication = {no},
journal = {Proceedings of the Royal Society of Edinburgh Section A-Mathematics},
month = {Jan},
pages = {57-69},
peerreviewed = {Yes},
title = {{ON} {BOUNDARY} {FEEDBACK} {STABILISABILITY} {OF} {A} {VISCOELASTIC} {BEAM}},
url = {https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/on-boundary-feedback-stabilisability-of-a-viscoelastic-beam/F4A796392C45ECEEE3A0142E33FAA739},
volume = {114},
year = {1990}
}
@article{faucris.119952184,
abstract = {We consider a tripod as an exemplaric network of strings. We know that such a network is exactly controllable in the natural finite energy space, if, e.g., the simple nodes are controlled by Dirichlet controls in (HL)-L-1(0, T). Assume that we want to calculate the corresponding norm-minimal controls using semi-discretization in space. We then obtain a system of coupled second-order-in-time ordinary differential equations with three control inputs. Controllability of the latter system can easily been checked by Kalman's rank condition on each space discretization level h. One expects, as h tends to zero, that the exact controllability of the continuous system is revealed. This expectation is frustrated, as has been shown by Infante and Zuazua (1998) for a. single string and by Zuazua (1999) for a membrane. Indeed, it was shown there that uniformity of observability estimates is lost in the limit. On the other hand, spectral filtering allows to cure this pathology. We show in this paper that similar results hold for our string network. The generalization to arbitrary networks of strings in the out-of-the-plane as well as in the in-plane or 3-d-setup is then a technical matter. Therefore, this paper essentially extends the existing results to semidiscretizations of wave equations on arbitrary irregular computational grids.},
author = {Brauer, U. and Leugering, Günter},
faupublication = {no},
journal = {Control and Cybernetics},
keywords = {network of strings;semidiscretization;lack of uniform observability;filtering},
month = {Jan},
pages = {421-447},
peerreviewed = {Yes},
title = {{On} boundary observability estimates for semi-discretizations of a dynamic network of elastic strings},
url = {http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-article-BAT2-0001-1167},
volume = {28},
year = {1999}
}
@article{faucris.106690364,
author = {Hante, Falk and Sigalotti, Mario and Tucsnak, Marius},
doi = {10.1016/j.jde.2012.01.037},
faupublication = {no},
journal = {Journal of Differential Equations},
pages = {5569--5593},
peerreviewed = {Yes},
title = {{On} conditions for asymptotic stability of dissipative infinite-dimensional systems with intermittent damping},
volume = {252},
year = {2012}
}
@incollection{faucris.117910584,
abstract = {A decomposition-method introduced in [Le1] is used to decompose the rigid-body motion from the elastic vibration of a slowly rotating beam. On the base of the transformed system, a controller is constructed that steers all oscillations of the beam to rest in finite time. In addition, the beam is thereby driven to zero angular velocity. A second result is concerned with strong feed-back stabilizability.},
address = {Berlin; Heidelberg},
author = {Leugering, Günter},
booktitle = {Optimal Control of Partial Differential Equations - Proceedings of the IFIP WG 7.2 International Conference Irsee, April 9–12, 1990},
doi = {10.1007/BFb0043223},
editor = {Prof. Karl-Heinz Hoffmann; Prof. Werner Krabs},
faupublication = {no},
isbn = {978-3-540-46883-7},
month = {Jan},
pages = {182-191},
peerreviewed = {unknown},
publisher = {New York; Springer; 1999},
series = {Lecture Notes in Control and Information Sciences},
title = {{ON} {CONTROL} {AND} {STABILIZATION} {OF} {A} {ROTATING} {BEAM} {BY} {APPLYING} {MOMENTS} {AT} {THE} {BASE} {ONLY}},
url = {http://link.springer.com/chapter/10.1007/BFb0043223},
volume = {149},
year = {1991}
}
@incollection{faucris.117911464,
abstract = {We consider a planar graph representative of the reference configuration of a network of elastic prestretched strings coupled at the vertices of that graph. Some or all of the vertices may carry a point mass, and at those nodes dry friction on the plane may occur. We briefly describe the model and some results on well-posedness and control of such systems obtained in the literature. We then introduce a dynamic domain decomposition based on a Steklov-Poincaré-type operator. The analysis is given for the time-domain and the frequency-domain. Optimal control and problems of exact controllability are formulated and investigated in terms of the decoupling procedure.},
address = {Basel},
author = {Leugering, Günter},
booktitle = {Control and Estimation of Distributed Parameter Systems - International Conference in Vorau, Austria, July 14-20, 1996},
doi = {10.1007/978-3-0348-8849-3{\_}15},
editor = {W. Desch; F. Kappel; K. Kunisch},
faupublication = {no},
isbn = {978-3-0348-8849-3},
keywords = {dynamic domain decomposition;strings;networks;joint masses;dry friction;Steklov-Poincare-operators for networks;differential-delay systems;optimal control;controllability; 93C20; 93C80; 93B05; 65N55},
month = {Jan},
pages = {191-205},
peerreviewed = {unknown},
publisher = {Birkhäuser},
series = {International Series of Numerical Mathematics},
title = {{On} dynamic domain decomposition of controlled networks of elastic strings and joint-masses},
url = {http://link.springer.com/chapter/10.1007/978-3-0348-8849-3{\_}15},
volume = {126},
year = {1998}
}
@article{faucris.107401404,
abstract = {This paper is concerned with the analysis of equilibrium problems for two-dimensional elastic bodies with thin rigid inclusions and cracks. Inequality-type boundary conditions are imposed at the crack faces providing a mutual non-penetration between the crack faces. A rigid inclusion may have a delamination, thus forming a crack with non-penetration between the opposite faces. We analyze variational and differential problem formulations. Different geometrical situations are considered, in particular, a crack may be parallel to the inclusion as well as the crack may cross the inclusion, and also a deviation of the crack from the rigid inclusion is considered. We obtain a formula for the derivative of the energy functional with respect to the crack length for considering this derivative as a cost functional. An optimal control problem is analyzed to control the crack growth.},
author = {Khludnev, A. M. and Leugering, Günter},
doi = {10.1002/mma.1308},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
pages = {1955--1967},
peerreviewed = {Yes},
title = {{On} elastic bodies with thin rigid inclusions and cracks},
volume = {33},
year = {2010}
}
@article{faucris.123700984,
abstract = {This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions. Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval. © 2012 Fudan University and Springer-Verlag Berlin Heidelberg.},
author = {Leugering, Günter and Schmidt, Georg E.P.J.},
doi = {10.1007/s11401-011-0693-9},
faupublication = {yes},
journal = {Chinese Annals of Mathematics Series B},
keywords = {Controllability; Network; Nonlinear strings; Quasilinear system of hyperbolic equations},
pages = {33-60},
peerreviewed = {Yes},
title = {{On} exact controllability of networks of nonlinear elastic strings in 3-dimensional space},
volume = {33},
year = {2012}
}
@incollection{faucris.122685684,
abstract = {In these notes we want to present some control strategies for dynamic networks of strings and beams in those situations where the classical concepts of exact or approximate controllability fail. This is, in particular, the case for networks containing circuits. Generically, a residual motion settles in such circuits, even if all nodes are subject to controls. In those situations we resort to controls which direct the flux of energy. Using such controls in a network, we are able to steer the entire energy to preassigned parts of the structure. In practice these parts are more massive and can absorb energy more easily than the fragile elements. We also provide numerical evidence for the control strategies discussed in these notes. The material is related to joint work with J.E. Lagnese and E.G.P.G. Schmidt, and is essentially included [14].},
address = {Basel},
author = {Leugering, Günter},
booktitle = {Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena - International Conference in Vorau (Austria), July 18–24, 1993},
doi = {10.1007/978-3-0348-8530-0{\_}17},
editor = {W. Desch; F. Kappel; K. Kunisch},
faupublication = {no},
isbn = {978-3-0348-8530-0},
keywords = {absorbing;directing and nonlinear controls;disappearing solutions;numerical simulation; 39C20; 39B52; 65M06; 65M60},
month = {Jan},
pages = {301-326},
peerreviewed = {unknown},
publisher = {Birkhäuser},
series = {ISNM International Series of Numerical Mathematics},
title = {{On} feedback controls for dynamic networks of strings and beams and their numerical simulation},
url = {http://link.springer.com/chapter/10.1007/978-3-0348-8530-0{\_}17},
volume = {118},
year = {1994}
}
@inproceedings{faucris.117912344,
abstract = {The authors describe a general model for vibrating networks and show how the model applies to networks of elastic strings or Timoshenko beams. They indicate how hyperbolic energy estimates for first-order systems yield the a priori estimates needed to prove exact controllability and stabilizability. They show how the model can be generalized to allow mixed networks of strings and beams. They also discuss generalizations of the Timoshenko beam and their relation on the present model.},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {Decision and Control},
date = {1992-12-16/1992-12-18},
doi = {10.1109/CDC.1992.371260},
faupublication = {no},
isbn = {0-7803-0872-7},
keywords = {Yield estimation, Controllability},
month = {Jan},
pages = {3003-3008},
peerreviewed = {unknown},
publisher = {IEEE Xplore},
title = {{ON} {HYPERBOLIC} {SYSTEMS} {ASSOCIATED} {WITH} {THE} {MODELING} {AND} {CONTROL} {OF} {VIBRATING} {NETWORKS}},
url = {http://ieeexplore.ieee.org/document/371260/},
year = {1992}
}
@inproceedings{faucris.120849784,
abstract = {We consider a system of 1-d-diffusion-convection equations on graphs as being representative of flow or transport problems in channel, pipeline or root-systems appearing in many applications. Such systems are subject to controls the effect of which one wants to optimize. In these notes we discuss the mathematical framework of typical optimal control problems of such systems on graphs. We focus on singular perturbations with respect to diffusion and on the numerical implementation.},
author = {Leugering, Günter and Fischer, Thorsten},
faupublication = {yes},
month = {Jan},
pages = {69-97},
peerreviewed = {unknown},
title = {{On} instantaneous control of singularly perturbed hyperbolic equations on graphs},
volume = {219},
year = {2001}
}
@incollection{faucris.106894304,
address = {Hildesheim},
author = {Rathmann, Wigand and von Schroeders, Nicolai},
booktitle = {Medien im Mathematikunterricht},
editor = {Stephanie Gleich},
faupublication = {yes},
isbn = {978-3-88120-842-0},
pages = {39-56},
peerreviewed = {unknown},
publisher = {Franzbecker},
series = {MaMut Materialien für den Mathematikunterricht},
title = {{Online}-{Auswertungsverfahren} {STACK}},
volume = {6},
year = {2018}
}
@inproceedings{faucris.111074964,
abstract = {We consider a network of Euler-Bernoulli- and Rayleigh-beams. For the sake of simplicity, we concentrate on scalar displacements coupled to torsion. We show that the model is well-posed in appropriate ramification spaces. We then describe a dynamic nonoverlapping domain decomposition procedure of the network into its individual edges and provide a proof of convergence. Further, we formulate typical optimal control problems, related to exact controllability. The optimality system is solved using conjugate gradients. Various numerical examples illustrate the method.},
author = {Leugering, Günter and Rathmann, Wigand},
faupublication = {yes},
keywords = {Euler-Bernoulli- and Rayleigh beams;network models;nonoverlapping domain decompositions;optimal controls},
month = {Jan},
pages = {199-232},
peerreviewed = {unknown},
title = {{On} modeling, analysis and simulation of optimal control problems for dynamic networks of {Euler}-{Bernoulli}- and {Rayleigh}-beams},
volume = {218},
year = {2001}
}
@incollection{faucris.114041004,
address = {New York},
author = {Rathmann, Wigand and Leugering, Günter},
booktitle = {Control of Nonlinear Distributed Parameter Systems},
editor = {Chen G, Lasiecka I, Zhou J},
faupublication = {no},
peerreviewed = {unknown},
publisher = {Marcel Dekker Inc},
series = {Lecture Notes in Pure and Applied Mathematics Series},
title = {{On} {Modelling}, {Analysis} and {Simulation} of {Optimal} {Control} {Problems} of {Euler}-{Bernoulli}- and {Rayleigh}-{Beams}},
year = {2001}
}
@article{faucris.118521744,
abstract = {A shape optimization problem in three spatial dimensions for an elasto-dynamic piezoelectric body coupled to an acoustic chamber is introduced. Well-posedness of the problem is established and first order necessary optimality conditions are derived in the framework of the boundary variation technique. In particular, the existence of the shape gradient for an integral shape functional is obtained, as well as its regularity, sufficient for applications e.g. in modern loudspeaker technologies. The shape gradients are given by functions supported on the moving boundaries. The paper extends results obtained by the authors in (Math. Methods Appl. Sci. 33(17):2118–2131, 2010) where a similar problem was treated without acoustic coupling.},
author = {Leugering, Günter and Novotny, A. A. and Menzala, G. Perla and Sokolowski, J.},
doi = {10.1007/s00245-011-9148-7},
faupublication = {yes},
journal = {Applied Mathematics and Optimization},
pages = {441--466},
peerreviewed = {Yes},
title = {{On} {Shape} {Optimization} for an {Evolution} {Coupled} {System}},
volume = {64},
year = {2011}
}
@article{faucris.117913444,
abstract = {We study the limiting behavior of an optimal control problem for a linear elliptic equation subject to control and state constraints. Each constituent of the mathematical description of such an optimal control problem may depend on a small parameter epsilon. We study the limit of this problem when epsilon --> 0 in the framework of variational S-convergence which generalizes the concept of F-convergence. We also introduce the notion of G*-convergence generalizing the concept of G-convergence to operators. with constraints. We show convergence of the sequence of optimal control problems and identify its limit. We then apply the theory to an elliptic problem on a perforated domain.},
author = {Leugering, Günter and Kogut, Peter I.},
doi = {10.4171/ZAA/1023},
faupublication = {yes},
journal = {Zeitschrift für Analysis und ihre Anwendungen},
keywords = {homogenization;S-convergence;optimal control},
month = {Jan},
pages = {395-429},
peerreviewed = {Yes},
title = {{On} {S}-homogenization of an optimal control problem with control and state constraints},
url = {https://www.ems-ph.org/journals/show{\_}abstract.php?issn=0232-2064&vol=20&iss=2&rank=9},
volume = {20},
year = {2001}
}
@incollection{faucris.106691024,
address = {Berlin},
author = {Hante, Falk and Amin, Saurabh and Bayen, Alexandre M.},
booktitle = {Hybrid systems: computation and control},
doi = {10.1007/978-3-540-78929-1{\_}44},
faupublication = {yes},
pages = {602--605},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Comput. Sci.},
title = {{On} stability of switched linear hyperbolic conservation laws with reflecting boundaries},
volume = {4981},
year = {2008}
}
@article{faucris.115625004,
abstract = {Using the concept of contingent epiderivative, we generalize the notion of subdifferential to a cone-convex set-valued map. Properties of the subdifferential are presented and an optimality condition is discussed.},
author = {Jahn, Johannes and Baier, J.},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Convex analysis; Set-valued analysis; Subdifferentials; Vector optimization},
note = {UnivIS-Import:2015-03-05:Pub.1999.nat.dma.pama21.onsubd},
pages = {233-240},
peerreviewed = {Yes},
title = {{On} {Subdifferentials} of {Set}-{Valued} {Maps}},
volume = {100},
year = {1999}
}
@article{faucris.117913664,
abstract = {In this paper a general linear model for vibrating networks of one-dimensional elements is derived. This is applied to various situations including nonplanar networks of beams modelled by a three-dimensional variant on the Timoshenko beam, described for the first time in this paper. The existence and regularity of solutions is established for all the networks under consideration. The methods of first-order hyperbolic systems are used to obtain estimates from which exact controllability follows for networks containing no closed loops.},
author = {Langnese, John E. and Leugering, Günter and Schmidt, E. J. P. Georg},
doi = {10.1017/S0308210500029206},
faupublication = {no},
journal = {Proceedings of the Royal Society of Edinburgh Section A-Mathematics},
month = {Jan},
pages = {77-104},
peerreviewed = {Yes},
title = {{ON} {THE} {ANALYSIS} {AND} {CONTROL} {OF} {HYPERBOLIC} {SYSTEMS} {ASSOCIATED} {WITH} {VIBRATING} {NETWORKS}},
url = {https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/on-the-analysis-and-control-of-hyperbolic-systems-associated-with-vibrating-networks/92C650CDE4C03DF26D6009C6E5B61A6E},
volume = {124},
year = {1994}
}
@incollection{faucris.123354044,
address = {Berlin},
author = {Jahn, Johannes and Klose, Jürgen and Merkel, A.},
booktitle = {Advances in Optimization - Proceedings, Lambrecht, FRG, 1991},
editor = {W. Oettli, D. Pallaschke},
faupublication = {yes},
note = {UnivIS-Import:2015-04-20:Pub.1992.nat.dma.pama21.onthea},
pages = {478-491},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Economics and Mathematical Systems},
title = {{On} the {Application} of a {Method} of {Reference} {Point} {Approximation} to {Bicriterial} {Optimization} {Problems} in {Chemical} {Engineering}},
volume = {382},
year = {1992}
}
@article{faucris.122686784,
abstract = {A problem of image registration is considered in the context of optimal mass transportation. The properties and limitations of an optimal image transportation are analyzed. A modified formulation of this approach is proposed in order to overcome the morphing effect. Finally, a fast and simple scale-space approach for the new formulation is introduced, and numerical examples are presented.},
author = {Museyko, Oleg and Stiglmayr, Michael and Klamroth, Kathrin and Leugering, Günter},
doi = {10.1137/080721522},
faupublication = {yes},
journal = {Siam Journal on Imaging Sciences},
keywords = {image registration;image morphing;optimal mass transportation;Monge-Kantorovich problem; 94A08; 92C55; 49N99},
month = {Jan},
pages = {1068-1097},
peerreviewed = {Yes},
title = {{On} the {Application} of the {Monge}-{Kantorovich} {Problem} to {Image} {Registration}},
url = {http://epubs.siam.org/doi/abs/10.1137/080721522?journalCode=sjisbi},
volume = {2},
year = {2009}
}
@article{faucris.120147984,
abstract = {This paper works out connections between semidefinite optimization and vector optimization. It is shown that well-known semidefinite optimization problems are scalarized versions of a general vector optimization problem. This scalarization leads to the minimization of the trace or the maximal eigenvalue. © Taru Publications.},
author = {Jahn, Johannes and Carosi, L. and Martein, L.},
doi = {10.1080/09720502.2003.10700341},
faupublication = {yes},
journal = {Journal of Interdisciplinary Mathematics},
note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.pama21.xxx},
pages = {219-229},
peerreviewed = {unknown},
title = {{On} the {Connections} between {Semidefinite} {Optimization} and {Vector} {Optimization}},
volume = {6},
year = {2003}
}
@inproceedings{faucris.117915204,
abstract = {The authors introduce nonlinear equations describing the vibrations in space of networks of elastic strings and beams. Linearization about an equilibrium configuration yields a hyperbolic system of linear equations coupled by conditions at the multiple nodes where several network members meet. The authors study the controllability of these systems by controls exercised at some nodes. The multiplier method yields a priori inequalities guaranteeing exact controllability, and hence stabilizability, for certain rudimentary networks.},
author = {Leugering, Günter and Schmidt, E. J. P. Georg},
booktitle = {Decision and Control, 1989., Proceedings of the 28th IEEE Conference},
date = {1989-12-13/1989-12-15},
doi = {10.1109/CDC.1989.70580},
editor = {IEEE},
faupublication = {no},
keywords = {Nonlinear equations; Potential energy; Mathematics; Controllability; Control systems; Mathematical model; Kinetic energy; Partial differential equations; Statistics; Councils},
month = {Jan},
pages = {2287-2290},
peerreviewed = {unknown},
publisher = {IEEE Xplore},
title = {{ON} {THE} {CONTROL} {OF} {NETWORKS} {OF} {VIBRATING} {STRINGS} {AND} {BEAMS}},
url = {http://ieeexplore.ieee.org/document/70580/},
year = {1989}
}
@article{faucris.119866164,
author = {Jahn, Johannes},
faupublication = {yes},
journal = {Journal of Multi-Criteria Decision Analysis},
note = {UnivIS-Import:2015-03-05:Pub.1997.nat.dma.pama21.onthed},
pages = {17-24},
peerreviewed = {Yes},
title = {{On} the {Determination} of {Minimal} {Facets} and {Edges} of a {Polyhedral} {Set}},
volume = {6},
year = {1997}
}
@article{faucris.118531644,
abstract = {We investigate the occurrence of self-penalization in topology optimization problems for piezoceramicmechanical composites. Our main goal is to give physical interpretations for this phenomenon, i.e., to study the question why for various problems intermediate material values are not optimal in the absence of explicit penalization of the pseudo densities. In order to investigate this effect numerical experiments for several static and/or dynamic actuator and sensor objective functions are performed and their respective results are compared. The objective functions are mean transduction, displacement, sound power, electric potential, electric energy, energy conversion and electric power.},
author = {Wein, Fabian and Kaltenbacher, Manfred and Kaltenbacher, Barbara and Leugering, Günter and Bänsch, Eberhard and Schury, Fabian},
doi = {10.1007/s00158-010-0570-2},
faupublication = {yes},
journal = {Structural and Multidisciplinary Optimization},
pages = {405-417},
peerreviewed = {Yes},
title = {{On} the effect of self-penalization of piezoelectric composites in topology optimization},
volume = {43},
year = {2011}
}
@article{faucris.245142909,
abstract = {This article addresses the numerical simulation and optimization of the optical properties of mono-layered nano-particulate films. The particular optical property of interest is the so-called haze factor, for which a model close to an experimental setup is derived. The numerical solution becomes very involved due to the resulting size of computational domain in comparison to the wave length, rendering the direct simulation method infeasible. As a remedy, a hybrid method is suggested, which in essence consistently combines analytical solutions for the far field with finite element-based solutions for the near field. Using a series of algebraic reformulations, a model with an off- and online component is developed, which results in the computational complexity being reduced by several orders of magnitude. Based on the suggested hybrid numerical scheme, which is not limited to the haze factor as objective function, structural optimization problems covering geometrical and topological parametrizations are formulated. These allow the influence of different particle arrangements to be studied. The article is complemented by several numerical experiments underlining the strength of the method.},
author = {Semmler, Johannes and Stingl, Michael},
doi = {10.1007/s00158-020-02754-6},
faupublication = {yes},
journal = {Structural and Multidisciplinary Optimization},
keywords = {Finite element method; Gradient-based optimization; Haze factor; Maxwell’s equation; Particle scattering; Vector spherical harmonics},
note = {CRIS-Team Scopus Importer:2020-11-13},
peerreviewed = {Yes},
title = {{On} the efficient optimization of optical properties of particulate monolayers by a hybrid finite element approach},
year = {2020}
}
@article{faucris.119552224,
abstract = {We present an asymptotic approach to find optimal rotations of orthotropic material inclusions inside an isotropic linear elastic matrix. We compute approximate optimal solutions with respect to compliance and a stress based cost functional. We validate the local and global quality of the candidate solutions by means of finite element based parametric optimization algorithms. In particular, we devise a lower bound algorithm based on the free material optimization approach. Several numerical experiments are performed for different traction scenario},
author = {Schury, Fabian and Greifenstein, Jannis and Leugering, Günter and Stingl, Michael},
doi = {10.1007/s11081-014-9262-x},
faupublication = {yes},
journal = {Optimization and Engineering},
pages = {225-246},
peerreviewed = {Yes},
title = {{On} the efficient solution of a patch problem with multiple elliptic inclusions},
volume = {16},
year = {2015}
}
@article{faucris.121727144,
abstract = {The practice of production of composite materials with thin fibers requires a correct description of problems of the equilibrium of elastic bodies containing thin rigid inclusions. Of large importance is also an adequate description of the interaction of thin inclusions with cracks in an elastic body. As is known, inclusions can delaminate from the matrix, thereby forming a crack in the elastic body. A traditional approach to the description of cracks in elastic bodies consists in the use of equality-type boundary conditions at the crack faces. This approach frequently leads to unphysical results; for example, the corresponding solutions can yield a mutual penetration of the crack faces (see, e.g., [1, 2]). In the recent years, there was performed a wide cycle of investigations in the theory of cracks with boundary conditions corresponding to the mutual nonpenetration of the crack edges. In this case, the boundary conditions at the crack faces have the form of a set of equalities and inequalities. For acquaintance with such models, one can turn to [3, 4], where numerous appropriate references can be found. In this works, we suggest a model of an elastic body containing thin rigid inclusions with a property of delamination. For describing the delamination, we use inequality-type boundary conditions eliminating the mutual penetration of the crack faces.},
author = {Leugering, Günter and Khludnev, A. M.},
doi = {10.1134/S1028335810010040},
faupublication = {yes},
journal = {Doklady Physics},
pages = {18--22},
peerreviewed = {Yes},
title = {{On} the equilibrium of elastic bodies containing thin rigid inclusions},
volume = {55},
year = {2010}
}
@misc{faucris.107879244,
author = {Jahn, Johannes and Eibenstein, F. and Leitmann, G.},
faupublication = {no},
note = {UnivIS-Import:2015-03-05:Pub.1984.nat.dma.pama21.ontheg},
peerreviewed = {automatic},
title = {{On} the {Global} {Asymptotic} {Stabilization} of {Nonlinear} {Systems}},
year = {1984}
}
@article{faucris.124195324,
abstract = {In this article the authors continue the discussion in [9] about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measurements. In the present paper we prove the identifiability of varying densities of a planar tree-like network of strings along with the complete information on the graph, i.e. the lengths of the edges, the edge degrees and the angles between neighbouring edges. The results are achieved using the Titchmarch-Weyl function for the spectral problem and the Steklov-Poincare operator for the dynamic wave equation on the tree. The general result is obtained by a peeling argument which reduces the inverse problem layer-by-layer from the leaves to the clamped root of the tree. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim},
author = {Avdonin, Sergei and Abdon, Choque Rivero and Leugering, Günter and Mikhaylov, Victor},
doi = {10.1002/zamm.201400126},
faupublication = {yes},
journal = {ZAMM - Zeitschrift für angewandte Mathematik und Mechanik},
keywords = {Inverse problem;planar tree of strings;Titchmarch-Weyl-matrix;dynamic Steklov-Poincare operator;leaf-peeling method},
pages = {1490-1500},
peerreviewed = {Yes},
title = {{On} the inverse problem of the two-velocity tree-like graph},
volume = {95},
year = {2015}
}
@article{faucris.223557645,
abstract = {An example by Bastin and Coron illustrates that the boundary stabilization of 1-d hyperbolic systems with certain source terms is only possible if the length of the space interval is sufficiently small. We show that related phenomena also occur for networks of vibrating strings that are governed by the wave equation with a certain source term. It turns out that for a tree of strings with Neumann velocity feedback control at one boundary node and a homogeneous Dirichlet boundary condition at at least one boundary node and homogeneous Dirichlet or Neumann conditions at the other boundary nodes, boundary feedback stabilization is not possible if one of the strings is sufficiently long. However, if the number of strings in the tree is sufficiently large, also for arbitrarily short strings for certain parameters in the source term stabilization is not possible. The wave equation with source term that we consider is equivalent to a certain 2 ×2 system. For the examples that illustrate the limits of stabilizability, the matrix of the source term is not positive definite. However if the system parameters are chosen in such a way that the matrix is positive semi-definite, the tree of strings can be stabilized exponentially fast by the boundary feedback control for arbitrary long space intervals.},
author = {Gugat, Martin and Gerster, Stephan},
doi = {10.1016/j.sysconle.2019.104494},
faupublication = {yes},
journal = {Systems & Control Letters},
keywords = {Limits of stabilizability; Neumann feedback; Source terms; Stabilization; String networks},
note = {CRIS-Team Scopus Importer:2019-08-02},
peerreviewed = {Yes},
title = {{On} the limits of stabilizability for networks of strings},
volume = {131},
year = {2019}
}
@article{faucris.120144684,
abstract = {In this paper we investigate how to determine optimal locations of the microwave antennas being circularly ordered in a hyperthermia device. The heated area containing the tumor should have minimal volume. Based on a simple geometric model for the two and three dimensional case we develop algorithms for the computation of these volumes and present numerical results for the optimal location},
author = {Hutterer, Angelika and Jahn, Johannes},
faupublication = {yes},
journal = {Or Spectrum},
keywords = {Antenna optimization; Cancer medicine; Nonlinear programming},
note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.pama21.onthel},
pages = {397-412},
peerreviewed = {Yes},
title = {{On} the location of antennas for treatment planning in hyperthermia},
volume = {25},
year = {2003}
}
@article{faucris.108612284,
abstract = {Congrès

International conference on control of distributed parameter systems. 4 (1988)

1989, vol. 91, pp. 249-261 (12 ref.)},
author = {Leugering, Günter},
faupublication = {no},
journal = {International Series of Numerical Mathematics},
month = {Jan},
pages = {249-261},
peerreviewed = {unknown},
title = {{ON} {THE} {REACHABILITY} {PROBLEM} {OF} {A} {VISCOELASTIC} {BEAM} {DURING} {A} {SLEWING} {MANEUVER}},
volume = {91},
year = {1989}
}
@article{faucris.117458704,
abstract = {We consider the isothermal Euler equations without friction that simulate gas flow through a pipe. We consider the problem of boundary stabilisation of this system locally around a given stationary state. We present a feedback law that is linear in the physical variables and yields exponential decay of the system state. For the numerical solution of hyperbolic systems of conservation laws, the Jin-Xin relaxation scheme can be used. Therefore, we also consider the boundary stabilisation of the relaxation system by the linear Riemann feedback and present numerical examples that show the rapid exponential decay of the stabilised system. © 2012 Taylor & Francis Group, LLC.},
author = {Hirsch-Dick, Markus and Gugat, Martin and Herty, Michael and Steffensen, Sonja},
doi = {10.1080/00207179.2012.703787},
faupublication = {yes},
journal = {International Journal of Control},
keywords = {boundary feedback stabilisation; conservation laws; isothermal Euler equations; Lyapunov function; relaxation scheme},
note = {UnivIS-Import:2015-03-09:Pub.2012.nat.dma.zentr.onther},
pages = {1766-1778},
peerreviewed = {Yes},
title = {{On} the relaxation approximation of boundary control of the isothermal {Euler} equations},
volume = {85},
year = {2012}
}
@article{faucris.111754104,
author = {Hante, Falk},
doi = {10.1002/pamm.201610380},
faupublication = {yes},
journal = {Proceedings in Applied Mathematics and Mechanics},
pages = {783--784},
peerreviewed = {Yes},
title = {{On} the relaxation gap for {PDE} mixed-integer optimal control problems},
volume = {16},
year = {2016}
}
@article{faucris.286938922,
abstract = {We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uϵ) with respect to a small hole Bϵ around a given point x0 ϵ Bϵ ⊂ ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bϵ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.},
author = {Leugering, Günter and Novotny, Antonio André and Sokolowski, Jan},
doi = {10.2478/candc-2022-0015},
faupublication = {yes},
journal = {Control and Cybernetics},
keywords = {complex variables; Helmholtz problem; inverse problems; numerical methods; shape optimization; topological derivative},
note = {CRIS-Team Scopus Importer:2022-12-23},
pages = {227-248},
peerreviewed = {Yes},
title = {{On} the robustness of the topological derivative for {Helmholtz} problems and applications},
volume = {51},
year = {2022}
}
@article{faucris.122687444,
abstract = {We consider a star-graph as an examplary network, with elastic strings stretched along the edges. The network is allowed to perform out-of-the plane displacements. We consider such networks as being controlled at its simple nodes via Dirichlet conditions. The objective is to steer given initial data to final target data in a given time T with minimal control costs. This problem is discussed in the continuous as well as in the discrete case. We discuss an iterative domain decomposition technique and its discrete analogue. We prove convergence and show some numerical results. (C) 2000 Elsevier Science B.V. All rights reserved.},
author = {Leugering, Günter},
doi = {10.1016/S0377-0427(00)00307-1},
faupublication = {no},
journal = {Journal of Computational and Applied Mathematics},
keywords = {domain decomposition;networks of strings;optimal control;semi-discrete models},
pages = {133-157},
peerreviewed = {Yes},
title = {{On} the semi-discretization of optimal control problems for networks of elastic strings: global optimality systems and domain decomposition},
url = {http://www.sciencedirect.com/science/article/pii/S0377042700003071},
volume = {120},
year = {2000}
}
@incollection{faucris.118857684,
address = {Heidelberg},
author = {Jahn, Johannes},
booktitle = {Operations Research '93},
editor = {A. Bachem, U. Derigs, M. Jünger, R. Schrader},
faupublication = {yes},
note = {UnivIS-Import:2015-04-20:Pub.1994.nat.dma.pama21.onthes},
pages = {280-283},
peerreviewed = {unknown},
publisher = {Physica},
title = {{On} the {Solution} of {Linear} {Vector} {Optimization} {Problems} in the {Image} {Space}},
year = {1994}
}
@article{faucris.213483552,
abstract = {We study problems of optimal boundary control with systems governed by linear hyperbolic partial differential equations. The objective function is quadratic and given by an integral over the finite time interval (0, T) that depends on the boundary traces of the solution. If the time horizon T is sufficiently large, the solution of the dynamic optimal boundary control problem can be approximated by the solution of a steady state optimization problem. We show that for T -> infinity the approximation error converges to zero in the sense of the norm in L-2 (0, 1) with the rate 1/T, if the time interval (0, T) is transformed to the fixed interval (0, 1). Moreover, we show that also for optimal boundary control problems with integer constraints for the controls the turnpike phenomenon occurs. In this case the steady state optimization problem also has the integer constraints. If T is sufficiently large, the integer part of each solution of the dynamic optimal boundary control problem with integer constraints is equal to the integer part of a solution of the static problem. A numerical verification is given for a control problem in gas pipeline operations.},
author = {Gugat, Martin and Hante, Falk},
doi = {10.1137/17M1134470},
faupublication = {yes},
journal = {SIAM Journal on Control and Optimization},
month = {Jan},
note = {CRIS-Team WoS Importer:2019-03-15},
pages = {264-289},
peerreviewed = {Yes},
title = {{ON} {THE} {TURNPIKE} {PHENOMENON} {FOR} {OPTIMAL} {BOUNDARY} {CONTROL} {PROBLEMS} {WITH} {HYPERBOLIC} {SYSTEMS}},
volume = {57},
year = {2019}
}
@article{faucris.122593064,
abstract = {The paper concerns the analysis of equilibrium problems for 2D elastic bodies with thin inclusions modeled in the framework of Timoshenko beams. The first focus is on the well-posedness of the model problem in a variational setting. Then delaminations of the inclusions are considered, forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The corresponding variational formulations together with weak and strong solutions are discussed. The model contains various physical parameters characterizing the mechanical properties of the inclusion, such as flexural and shear stiffness. The paper provides an asymptotic analysis of such parameters. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain rigid inclusions and cracks with the non-penetration conditions, respectively. Finally, exemplary networks of Timoshenko beams are considered as inclusions as well.},
author = {Khludnev, A. M. and Leugering, Günter},
doi = {10.1177/1081286513505106},
faupublication = {yes},
journal = {Mathematics and Mechanics of Solids},
keywords = {Thin elastic inclusion;Timoshenko beams;crack;delamination;non-penetration boundary condition},
pages = {495-511},
peerreviewed = {Yes},
title = {{On} {Timoshenko} thin elastic inclusions inside elastic bodies},
volume = {20},
year = {2015}
}
@article{faucris.107412624,
abstract = {In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.1002/mma.3257},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
pages = {n/a},
peerreviewed = {Yes},
title = {{Optimal} and approximate boundary controls of an elastic body with quasistatic evolution of damage},
year = {2014}
}
@book{faucris.122947704,
abstract = {This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.},
address = {Basel},
author = {Gugat, Martin},
doi = {10.1007/978-3-319-18890-4},
edition = {1},
faupublication = {yes},
isbn = {978-3-319-18889-8},
keywords = {Systems Theory, Control; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization},
peerreviewed = {unknown},
publisher = {Birkhäuser},
series = {SpringerBriefs in Control, Automation and Robotics},
title = {{Optimal} {Boundary} {Control} and {Boundary} {Stabilization} of {Hyperbolic} {Systems}},
url = {http://www.springer.com/us/book/9783319188898},
year = {2015}
}
@incollection{faucris.119025984,
abstract = {

In active flood hazard mitigation, lateral flow withdrawal is used to reduce the impact of flood waves in rivers. Through emergency side channels, lateral outflow is generated. The optimal outflow controls the flood in such a way that the cost of the created damage is minimized. The flow is governed by a networked system of nonlinear hyperbolic partial differential equations, coupled by algebraic node conditions. Two types of integrals appear in the objective function of the corresponding optimization problem: Boundary integrals (for example, to measure the amount of water that flows out of the system into the floodplain) and distributed integrals.

For the evaluation of the derivative of the objective function, we introduce an adjoint backwards system. For the numerical solution we consider a discretized system with a consistent discretization of the continuous adjoint system, in the sense that the discrete adjoint system yields the derivatives of the discretized objective function. Numerical examples are included.

}, address = {Basel}, author = {Gugat, Martin}, booktitle = {International Series of Numerical Mathematics}, doi = {10.1007/978-3-7643-7721-2{\_}4}, editor = {Karl-Heinz Hoffmann, Günter Leugering, Michael Hintermüller}, faupublication = {yes}, isbn = {978-3-7643-7721-2}, keywords = {St. Venant equations; subcritical states; adjoint system; optimal boundary control; necessary optimality conditions; classical solutions}, note = {UnivIS-Import:2015-04-20:Pub.2007.nat.dma.zentr.optima}, pages = {69-94}, peerreviewed = {unknown}, publisher = {Birkhäuser}, series = {Control of Coupled Partial Differential Equations}, title = {{Optimal} {Boundary} {Control} in {Flood} {Management}}, url = {http://link.springer.com/chapter/10.1007/978-3-7643-7721-2{\_}4}, volume = {155}, year = {2007} } @article{faucris.121019404, abstract = {The problem to control a finite string to the zero state in finite time from a given initial state by controlling the state at the two boundary points in such a way that the controls generate a continuous state is considered. The corresponding optimal control problem where the objective function is the L
The number of dual-career couples with children is growing fast. These

couples face various challenging problems of organizing their lifes, in par-

ticular connected with childcare and time-management. As a typical ex-

ample we study one of the difficult decision problems of a dual career

couple from the point of view of operations research with a particular

focus on gender equality, namely the location problem to find a family

home. This leads to techniques that allow to include the value of gender

equality in rational decision processes.

},
author = {Gugat, Martin and Abele-Brehm, Andrea and Klamroth, Kathrin},
faupublication = {yes},
keywords = {Dual Careec couples, Optimal Location Problem, Childcare Management},
peerreviewed = {automatic},
title = {{Optimal} location of family homes for dual career couples},
url = {http://www.optimization-online.org/DB{\_}HTML/2010/02/2547.html},
year = {2010}
}
@article{faucris.117325824,
abstract = {
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T, by minimizing an objective functional that is the convex sum of the L^{2}-norm of the control and of a boundary Neumann tracking term.

We provide an explicit solution of this optimal control problem, showing that if the weight of the tracking term is positive, then the optimal control action is concentrated at the beginning and at the end of the time interval, and in-between it decays exponentially. We show that the optimal control can actually be written in that case as the sum of an exponentially decaying term and of an exponentially increasing term. This implies that, if the time T is large, then the optimal trajectory approximately consists of three arcs, where the first and the third short-time arcs are transient arcs, and in the middle arc the optimal control and the corresponding state are exponentially close to 0. This is an example of a turnpike phenomenon for a problem of optimal boundary control. If T=+∞ (infinite time horizon problem), then only the exponentially decaying component of the control remains, and the norms of the optimal control action and of the optimal state decay exponentially in time. In contrast to this situation, if the weight of the tracking term is zero and only the control cost is minimized, then the optimal control is distributed uniformly along the whole interval [0,T] and coincides with the control given by the Hilbert Uniqueness Method.

In addition, we establish a similarity theorem stating that, for every T>0, there exists an appropriate weight λ<1 for which the optimal solutions of the corresponding finite horizon optimal control problem and of the infinite horizon optimal control problem coincide along the first part of the time interval [0,2]. We also discuss the turnpike phenomenon from the perspective of a general framework with a strongly continuous semi-group.

}, author = {Gugat, Martin and Trelat, Emmanuel and Zuazua, Enrique}, doi = {10.1016/j.sysconle.2016.02.001}, faupublication = {yes}, journal = {Systems & Control Letters}, keywords = {Vibrating string; Neumann boundary control; Turnpike phenomenon; Exponential stability; Energy decay; Exact control; Infinite horizon optimal control; Similarity theorem; Receding horizon}, pages = {61-70}, peerreviewed = {Yes}, title = {{Optimal} {Neumann} control for the {1D} wave equation: {Finite} horizon, infinite horizon, boundary tracking terms and the turnpike property}, volume = {90}, year = {2016} } @article{faucris.111889624, abstract = {In many control application, switching between different control devices occurs. Here the problem to control a finite string to the zero state in finite time by controlling the state at the two boundary points is considered, where at each moment in time one of the boundary controls must be switched off, that is its control value must be equal to zero. The corresponding optimal control problem where the objective function is the L}, author = {Semmler, Johannes and Bley, Karina and Klupp Taylor, Robin and Stingl, Michael and Vogel, Nicolas}, doi = {10.1002/adfm.201806025}, faupublication = {yes}, journal = {Advanced Functional Materials}, peerreviewed = {unknown}, title = {{Particulate} {Coatings} with {Optimized} {Haze} {Properties}}, url = {https://onlinelibrary.wiley.com/doi/full/10.1002/adfm.201806025}, volume = {5}, year = {2018} } @book{faucris.109705244, abstract = {A class of nonsmooth shape optimization problems for variational inequalities is considered. The variational inequalities model elliptic boundary value problems with the Signorini type unilateral boundary conditions. The shape functionals are given by the first order shape derivatives of the elastic energy. In such a way the singularities of weak solutions to elliptic boundary value problems can be characterized. An example in solid mechanics is given by the Griffith’s functional, which is defined in plane elasticity to measure SIF, the so-called stress intensity factor, at the crack tips. Thus, topological optimization can be used for passive control of singularities of weak solutions to variational inequalities. The Hadamard directional differentiability of metric the projection onto the positive cone in fractional Sobolev spaces is employed to the topological sensitivity analysis of weak solutions of nonlinear elliptic boundary value problems. The first order shape derivatives of energy functionals in the direction of specific velocity fields depend on the solutions to variational inequalities in a subdomain. A domain decomposition technique is used in order to separate the unilateral boundary conditions and the energy asymptotic analysis. The topological derivatives of nonsmooth integral shape functionals for variational inequalities are derived. Singular geometrical domain perturbations in an elastic body Ω are approximated by regular perturbations of bilinear forms in variational inequality, without any loss of precision for the purposes of the secondorder shape-topological sensitivity analysis. The second-order shape-topological directional derivatives are obtained for the Laplacian and for linear elasticity in two and three spatial dimensions. In the proposed method of sensitivity analysis, the singular geometrical perturbations ϵ→ω ⊂ Ω centred at x ∈ Ω are replaced by regular perturbations of bilinear forms supported on the manifold Γ ={|x−x|=R} in an elastic body, with R > ϵ > 0. The obtained expressions for topological derivatives are easy to compute and therefore useful in numerical methods of topological optimization for contact problems.}, author = {Leugering, Günter and Sokolowski, Jan and Zochowski, Antoni}, doi = {10.1007/978-3-319-30785-5{\_}4}, faupublication = {yes}, pages = {65-102}, peerreviewed = {unknown}, publisher = {Springer International Publishing}, title = {{Passive} control of singularities by topological optimization: {The} second-order mixed shape derivatives of energy functionals for variational inequalities}, volume = {109}, year = {2016} } @article{faucris.107372804, abstract = {In these notes we consider PDE-constrained optimization in the context of advanced materials. We give examples for optimization and control in the coefficients, free material optimization, topology optimization, shape optimization in elastic and piezo-electric materials. We explain some approaches to metamaterials, in particular for auxetic materials}, author = {Leugering, Günter and Stingl, Michael}, doi = {10.1002/gamm.201010016}, faupublication = {yes}, journal = {GAMM-Mitteilungen}, keywords = {piezoelectricity; electromechanical interaction; shape sensitivity analysis}, pages = {209-229}, peerreviewed = {unknown}, title = {{PDE}-constrained optimization for advanced materials}, url = {http://onlinelibrary.wiley.com/doi/10.1002/gamm.201010016/epdf}, volume = {33}, year = {2010} } @article{faucris.121354464, author = {Gugat, Martin}, doi = {10.1137/080725921}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, keywords = {wave equation, Tychonov regularization, PDE constrained optimization, penal- ization, exact penalty, exact controllability, state constraints, smoothed exact penalty, speed of convergence, hyperbolic PDE, optimal control}, note = {UnivIS-Import:2015-03-09:Pub.2009.nat.dma.zentr.penalt}, pages = {3026-3051}, peerreviewed = {Yes}, title = {{Penalty} {Techniques} for {State} {Constrained} {Optimal} {Control} {Problems} with the {Wave} {Equation}}, url = {http://epubs.siam.org/doi/abs/10.1137/080725921}, volume = {48}, year = {2009} } @incollection{faucris.123288264, abstract = {We compare the quality and generation performance of the optimal control sequence produced by the software frameworks BlueM.MPC and Lamatto.}, author = {Heusch, Steffen and Hild, Johannes and Leugering, Günter and Ostrowski, Manfred}, booktitle = {Mathematical Optimization of Water Networks}, doi = {10.1007/978-3-0348-0436-3{\_}9}, editor = {Birkhäuser Basel}, faupublication = {yes}, isbn = {978-3-0348-0435-6}, pages = {151-165}, peerreviewed = {unknown}, publisher = {Springer Basel}, series = {International Series of Numerical Mathematics}, title = {{Performance} and {Comparison} of {BlueM}.{MPC} and {Lamatto}}, volume = {162}, year = {2012} } @incollection{faucris.120448064, author = {Jahn, Johannes}, booktitle = {Methods of Operations Research}, faupublication = {yes}, note = {UnivIS-Import:2015-03-05:Pub.1987.nat.dma.pama21.proble}, pages = {51-59}, peerreviewed = {unknown}, title = {{Problems} of {Vector} {Optimization}}, volume = {57}, year = {1987} } @article{faucris.118517124, abstract = {In this contribution the identification of new reaction conditions for the production of nearly monodisperse silicon nanoparticles via the pyrolysis of monosilane in a hot wall reactor is considered. For this purpose a full finite volume model has been combined with a state-of-the-art trust-region optimisation algorithm for process control. Verified against experimental data, specific process conditions are determined accomplishing a versatile range of prescribed product properties. The main achievement of the optimisation is the possibility to control the different mechanisms in the particle formation process by mainly adjusting the temperature profile. Due to a successful separation of the nucleation and growth process, significantly narrower particle size distributions are obtained. Moreover, the presented optimisation framework establishes rate constants based on measured data.}, author = {Gröschel, Michael and Koermer, Richard and Walther, Maximilian and Leugering, Günter and Peukert, Wolfgang}, doi = {10.1016/j.ces.2012.01.035}, faupublication = {yes}, journal = {Chemical Engineering Science}, pages = {181--194}, peerreviewed = {Yes}, title = {{Process} control strategies for the gas phase synthesis of silicon nanoparticles}, volume = {73}, year = {2012} } @article{faucris.222304913, author = {Geiger, Manfred and Meßner, Arthur and Engel, Ulf}, faupublication = {yes}, journal = {Production Engineering}, note = {LFT Import::2019-07-15 (650)}, peerreviewed = {Yes}, title = {{Production} of microparts - size effects in bulk metal {Forming}, similarity theory.}, year = {1996} } @incollection{faucris.115535684, address = {Rocquencourt}, author = {Jahn, Johannes}, booktitle = {Third Franco-German Conference in Optimization}, faupublication = {no}, note = {UnivIS-Import:2015-04-17:Pub.1985.nat.dma.pama21.proper}, pages = {27-28}, peerreviewed = {unknown}, publisher = {INRIA Report}, title = {{Properly} {Minimal} {Elements} of a {Set}}, year = {1985} } @article{faucris.119588304, author = {Truong, Xuan Duc Ha and Jahn, Johannes}, faupublication = {yes}, journal = {Journal of Nonlinear and Convex Analysis}, pages = {415 - 429}, peerreviewed = {Yes}, title = {{Properties} of {Bishop}-{Phelps} cones}, volume = {18}, year = {2017} } @article{faucris.110637824, abstract = {If a fractional program does not have a unique solution or the feasible set is unbounded, numerical difficulties can occur. By using a prox-regularization method that generates a sequence of auxiliary problems with unique solutions, these difficulties are avoided. Two regularization methods are introduced here. They are based on Dinkelbach-type algorithms for generalized fractional programming, but use a regularized parametric auxiliary problem. Convergence results and numerical examples are presented.}, author = {Gugat, Martin}, doi = {10.1023/A:1021759318653}, faupublication = {no}, journal = {Journal of Optimization Theory and Applications}, keywords = {differential correction method; Dinkelbach algorithm; Generalized fractional programs; ill-posed problems; linear convergence; prox-regularization}, note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.lama1.proxre}, pages = {691-722}, peerreviewed = {Yes}, title = {{Prox}-{Regularization} {Methods} for {Generalized} {Fractional} {Programming}}, url = {http://link.springer.com/article/10.1023/A:1021759318653}, volume = {99}, year = {1998} } @phdthesis{faucris.106824124, abstract = {We study the shallow water equations augmented with pollution transport in one space dimension on prismatic channels with nontrivial channel width. We use both, the characteristic and the weak formulation, to construct an explicit solution of the corresponding Riemann problem. This solution is an important ingredient for Godunov's Finite volume scheme, which is used to discretize a real world sewer system into a network of finite volume elements. We especially focus on a finite volume model for the network vertices, which implies weak coupling conditions at each vertex and is based on the solution of a transjunctional Riemann problem. In order to develop a process model for sewer systems of practical relevance, we introduce generalized numerical flux functions, which allow the modeling of wave reflections at nonprismatic channel junctions and walls. The generalized numerical flux functions also enable the modeling of controllable special structures like pumps, weirs and valves. The resulting process model is especially suited for real world sewer systems and is mathematically represented by a system of ordinary differential equations. The controllable process model is subject to an optimal control problem for real-time application. We discretize the process model with a general linear one-step scheme in time and use adjoint calculus to provide explicit formulas for the gradient and Hessian of the time discrete cost functional. We verify our approach with a self-written C++ application, which is tailored to optimize finite volume networks in real-time, and provide numerical results for two sewer systems, which are both based on practical application. We apply a receding horizon strategy to both test cases and compare the real-time control results with the previously computed solutions of an online control approach.}, author = {Hild, Johannes}, faupublication = {yes}, school = {Friedrich-Alexander-Universität Erlangen-Nürnberg}, title = {{Real}-{Time} {Control} of {Hydrodynamic} {Process} {Models} on {Finite} {Volume} {Networks}}, year = {2012} } @incollection{faucris.122351724, abstract = {A hydrodynamic process model based on shallow water equations is discretized on 1D-networks with the method of finite volumes. Based on the finite volumes we replace algebraic coupling conditions by a consistent finite volume junction model. We use discrete adjoint computation for one step Runge-Kutta schemes to generate fast and robust gradients for descent methods. We use the descent methods to generate an optimal control for an example network and discuss the computational results.}, author = {Hild, Johannes and Leugering, Günter}, booktitle = {Mathematical Optimization of Water Networks}, doi = {10.1007/978-3-0348-0436-3{\_}8}, editor = {Birkhäuser Basel}, faupublication = {yes}, isbn = {978-3-0348-0435-6}, pages = {pp 129-150}, peerreviewed = {unknown}, publisher = {Springer Basel}, series = {International Series of Numerical Mathematics}, title = {{Real}-{Time} {Control} of {Urban} {Drainage} {Systems}}, volume = {162}, year = {2012} } @book{faucris.109061964, address = {Berlin}, editor = {Jahn, Johannes and Krabs, W.}, faupublication = {yes}, note = {UnivIS-Import:2015-05-08:Pub.1987.nat.dma.pama21.dualit}, publisher = {Springer}, title = {{Recent} {Advances} and {Historical} {Development} of {Vector} {Optimization}}, year = {1987} } @article{faucris.115216464, abstract = {This paper presents a reference point approximation algorithm which can be used for the interactive solution of bicriterial nonlinear optimization problems with inequality and equality constraints. The advantage of this method is that the decision maker may choose arbitrary reference points in the criteria space. Moreover, a special tunneling technique is given for the computation of global solutions of certain subproblems. Finally, the proposed method is applied to a mathematical example and a problem in mechanical engineering. © 1992 Plenum Publishing Corporation.}, author = {Jahn, Johannes and Merkel, A.}, doi = {10.1007/BF00939894}, faupublication = {yes}, journal = {Journal of Optimization Theory and Applications}, keywords = {interactive methods; Multi-objective optimization}, note = {UnivIS-Import:2015-03-05:Pub.1992.nat.dma.pama21.refere}, pages = {87-103}, peerreviewed = {Yes}, title = {{Reference} {Point} {Approximation} {Method} for the {Solution} of {Bicriterial} {Nonlinear} {Optimization} {Problems}}, volume = {74}, year = {1992} } @article{faucris.117916084, abstract = {We present an algorithm that automatically registers one segmented contour in a frame of the video sequence to the contour in the next frame to derive discrete 2-D trajectories of PE vibrations. By concatenation of the obtained transformations this approach provides a total registration of PE segment contours. We suggest a mixed-integer programming formulation for the problem that combines an advanced outlier and deformation handling with the introduction of dummy points in regions that newly open up, and that includes normal information in the objective function to avoid unwanted deformations. Numerical experiments show that the implemented alternate convex search algorithm produces robust results which is demonstrated at the example of five high-speed recordings of laryngectomee subjects. (C) 2007 Elsevier B.V. All rights reserved.}, author = {Stiglmayr, Michael and Schwarz, Raphael and Klamroth, Kathrin and Leugering, Günter and Lohscheller, Jörg}, doi = {10.1016/j.media.2007.12.001}, faupublication = {yes}, journal = {Medical Image Analysis}, keywords = {substitute voice;PE segment;digital high-speed videos;point matching;shape registration;generalized assignment problem;2-D trajectories}, pages = {318-334}, peerreviewed = {Yes}, title = {{Registration} of {PE} segment contour deformations in digital high-speed videos}, url = {http://www.sciencedirect.com/science/article/pii/S1361841507001120}, volume = {12}, year = {2008} } @article{faucris.107398324, abstract = {In this contribution the optimal boundary control problem for a first order nonlinear, nonlocal hyperbolic PDE is studied. Motivated by various applications ranging from re-entrant manufacturing systems to particle synthesis processes, we establish the regularity of solutions for W1,p-data. Based on a general L2 tracking type cost functional, the existence, uniqueness, and regularity of the adjoint system in W1,p is derived using the special structure induced from the nonlocal flux function of the state equation. The assumption of W1,p - and not Lp-regularity comes thereby due to the fact that the adjoint equation asks for more regularity to be well defined. This problem is discussed in detail, and we give a solution by defining a special type of cost functional, such that the corresponding optimality system is well defined.}, author = {Gröschel, Michael and Keimer, Alexander and Leugering, Günter and Wang, Zhiqiang}, doi = {10.1137/120873832}, faupublication = {yes}, journal = {SIAM Journal on Control and Optimization}, pages = {2141--2163}, peerreviewed = {Yes}, title = {{Regularity} {Theory} and {Adjoint}-{Based} {Optimality} {Conditions} for a {Nonlinear} {Transport} {Equation} with {Nonlocal} {Velocity}}, volume = {52}, year = {2014} } @article{faucris.110992904, abstract = {

We consider *L* ^{∞}-norm minimal controllability problems for vibrating systems. In the common method of modal truncation controllability constraints are first reformulated as an infinite sequence of moment equations, which is then truncated to a finite set of equations. Thus, feasible controls are represented as solutions of moment problems.

In this paper, we propose a different approach, namely to replace the sequence of moment equations by a sequence of moment inequalities. In this way, the feasible set is enlarged. If a certain relaxation parameter tends to zero, the enlarged sets approach the original feasible set. Numerical examples illustrate the advantages of this new approach compared with the classical method of moments.

The introduction of moment inequalities can be seen as a regularization method, that can be used to avoid oscillatory effects. This regularizing effect follows from the fact that for each relaxation parameter, the whole sequence of eigenfrequencies is taken into account, whereas in the method of modal truncation, only a finite number of frequencies is considered.

}, author = {Gugat, Martin and Leugering, Günter}, doi = {10.1023/A:1015472323967}, faupublication = {no}, journal = {Computational Optimization and Applications}, keywords = {optimal control; exact controllability; eigenvalues; moment problem; moment inequalities; numerical algorithm; convergence}, note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.regula}, pages = {151-192}, peerreviewed = {Yes}, title = {{Regularization} of {L}-∞ optimal control problems for distributed parameter systems}, url = {http://link.springer.com/article/10.1023/A:1015472323967}, volume = {22}, year = {2002} } @article{faucris.109705684, abstract = {This paper concerns the generalization and regularization of a nonlinear scalarization method by Pascoletti and Serafini, [14], to abstract partially ordered Banach spaces. In particular, we put emphasis on the possibility that the ordering cone might have an empty interior. All this is motivated by applying the method to a vector optimization problem with PDE-constraints. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.}, author = {Leugering, Günter and Schiel, Ralph}, doi = {10.1002/gamm.201210014}, faupublication = {yes}, journal = {GAMM-Mitteilungen}, keywords = {Gerstewitz function; Nonlinear scalarization; Nonsolid ordering cones; Optimal control; Vector optimization}, pages = {209-225}, peerreviewed = {Yes}, title = {{Regularized} nonlinear scalarization for vector optimization problems with {PDE}-constraints}, volume = {35}, year = {2012} } @article{faucris.123654564, author = {Hante, Falk and Sager, Sebastian}, doi = {10.1007/s10589-012-9518-3}, faupublication = {yes}, journal = {Computational Optimization and Applications}, pages = {197--225}, peerreviewed = {Yes}, title = {{Relaxation} methods for mixed-integer optimal control of partial differential equations}, volume = {55}, year = {2013} } @inproceedings{faucris.120852424, abstract = {In this paper we consider some classes of discrete-continuous 2-D models in order to build a finite dimensional linear state space model of a gas distribution network. The models introduced are shown to be suitable for handling problems of optimal control of pressure and flow in gas transport units. The focus is on the development of a comprehensive optimization theory based on a 'constructive approach'. Moreover, an optimal feedback control problem is considered that is of interest in both systems theory and application.}, author = {Dymkou, Siarhei and Leugering, Günter and Jank, Gerhard}, booktitle = {Multidimensional (nD) Systems}, date = {2007-06-27/2007-06-29}, doi = {10.1109/NDS.2007.4509556}, editor = {IEEE}, faupublication = {yes}, keywords = {Pipelines; Mathematical model; State-space methods; Optimal control; Transportation; Large-scale systems; Optimization methods; Control theory; Fluid flow; Isothermal processes}, month = {Jan}, pages = {101-108}, peerreviewed = {unknown}, publisher = {IEEE Xplore}, title = {{Repetitive} processes modelling of gas transport networks}, url = {http://ieeexplore.ieee.org/document/4509556/}, year = {2007} } @inproceedings{faucris.122844744, author = {Gugat, Martin and Tucsnak, Marius and Sigalotti, Mario}, booktitle = {Proceedings of the 9th European Control Conference, Kos, Greece, 2007.}, date = {2007-07-02/2007-07-05}, doi = {10.23919/ECC.2007.7068766}, faupublication = {yes}, isbn = {978-3-9524173-8-6}, keywords = {vibrating string; boundary control; robustness; position term;}, note = {UnivIS-Import:2015-04-16:Pub.2007.nat.dma.zentr.robust}, pages = {-}, publisher = {IEEE}, title = {{Robustness} analysis for the boundary control of the string equation}, url = {https://ieeexplore.ieee.org/document/7068766}, venue = {Kos}, year = {2007} } @inproceedings{faucris.235431970, abstract = {Für ein besseres Verständnis helfen interaktive Inhalte weiter. Im
Bereich der Statistik oder der Darstellung von dreidimensionalen
Objekten fehlte bisher die Möglichkeit, dies direkt in Lernmodulen
einzubinden. Mit dem neuen Content-Element "SageMath-Cell" kann nun z.B.
direkt R-Code in Lernmodulen genutzt werden. SageMath ist ein
mathematisches Softwaresystem, das die Nutzung vieler
Open-Source-Pakete, wie Maxima oder R, zusammenfasst; es kann auch
Python genutzt werden. In diesem Workshop wird an Beispielen erprobt,
wie das Content-Element aus Autorensicht angewendet werden kann. Ihre
Ideen können Sie gerne mitbringen – und bitte auch Ihren Compute},
author = {Rathmann, Wigand and Copado Mejías, Jesús},
booktitle = {18. Internationale ILIAS-Konferenz},
date = {2019-09-26/2019-09-27},
faupublication = {yes},
peerreviewed = {unknown},
title = {{Sage} als {Content}-{Element} in {ILIAS} nutzen},
venue = {Dresden},
year = {2019}
}
@incollection{faucris.122402544,
address = {Wien},
author = {Jahn, Johannes},
booktitle = {Mathematics of Multi Objective Optimization},
editor = {P. Serafini},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1985.nat.dma.pama21.scalar},
pages = {45-88},
peerreviewed = {unknown},
publisher = {Springer},
title = {{Scalarization} in {Multi} {Objective} {Optimization}},
year = {1985}
}
@article{faucris.110288904,
abstract = {In this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem. This will be done for weakly minimal and minimal solutions, respectively. Finally the results will be applied to a certain class of approximation problems. © 1984 The Mathematical Programming Society, Inc.},
author = {Jahn, Johannes},
doi = {10.1007/BF02592221},
faupublication = {no},
journal = {Mathematical Programming},
keywords = {Approximation; Multi-Objective Programming; Vector Optimization},
note = {UnivIS-Import:2015-03-05:Pub.1984.nat.dma.pama21.scalar},
pages = {203-218},
peerreviewed = {Yes},
title = {{Scalarization} in {Vector} {Optimization}},
volume = {29},
year = {1984}
}
@article{faucris.116397864,
abstract = {In this paper, we propose second-order epiderivatives for set-valued maps. By using these concepts, second-order necessary optimality conditions and a sufficient optimality condition are given in set optimization. These conditions extend some known results in optimization. © 2005 Springer Science+Business Media, Inc.},
author = {Jahn, Johannes and Khan, Akhtar Ali and Zeilinger, P.},
doi = {10.1007/s10957-004-1841-0},
faupublication = {yes},
journal = {Journal of Optimization Theory and Applications},
keywords = {Optimality conditions; Second-order epiderivatives; Set optimization},
note = {UnivIS-Import:2015-03-09:Pub.2005.nat.dma.pama21.second},
pages = {331-347},
peerreviewed = {Yes},
title = {{Second}-{Order} {Optimality} {Conditions} in {Set} {Optimization}},
volume = {125},
year = {2005}
}
@phdthesis{faucris.108545404,
author = {Jahn, Johannes},
faupublication = {no},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{Sequentieller} {Innerer}-{Punkt}-{Algorithmus} zur {Lösung} nichtlinearer {Optimierungsprobleme}},
year = {1978}
}
@article{faucris.111888304,
abstract = {In this paper set-semidefinite optimization is introduced as a new field of vector optimization in infinite dimensions covering semidefinite and copositive programming. This unified approach is based on a special ordering cone, the so-called K-semidefinite cone for which properties are given in detail. Optimality conditions in the KKT form and duality results including the linear case are presented for K-semidefinite optimization problems. A penalty approach is developed for the treatment of the special constraint arising in K-semidefinite optimization problems. © Heldermann Verlag.},
author = {Eichfelder, Gabriele and Jahn, Johannes},
faupublication = {yes},
journal = {Journal of Convex Analysis},
keywords = {Convex analysis; Copositive programming; Semidefinite programming; Vector optimization},
note = {UnivIS-Import:2015-03-09:Pub.2008.nat.dma.pama21.setsem},
pages = {767-801},
peerreviewed = {Yes},
title = {{Set}-{Semidefinite} {Optimization}},
volume = {15},
year = {2008}
}
@incollection{faucris.122944404,
address = {Dordrecht},
author = {Jahn, Johannes},
booktitle = {Encyclopedia of Optimization},
editor = {C.A. Floudas, P.M. Pardalos},
faupublication = {yes},
note = {UnivIS-Import:2015-04-20:Pub.2001.nat.dma.pama21.setval},
pages = {3486 - 3488},
peerreviewed = {unknown},
publisher = {Kluwer},
title = {{Set}-{Valued} {Optimization}},
year = {2009}
}
@incollection{faucris.111077384,
abstract = {In this review article the theoretical foundations for shape-topological sensitivity analysis of elastic energy functional in bodies with nonlinear cracks and inclusions are presented. The results obtained can be used to determine the location and the shape of inclusions which influence in a desirable way the energy release at the crack tip. In contrast to the linear theory, where in principle, crack lips may mutually penetrate, here we employ nonlinear elliptic boundary value problems in non-smooth domains with cracks with non-penetration contact conditions across the crack lips or faces. A shape-topological sensitivity analysis of the associated variational inequalities is performed for the elastic energy functional. Topological derivatives of integral shape functionals for variational inequalities with unilateral boundary conditions are derived. The closed form results are obtained for the Laplacian and linear elasticity in two and three spatial dimensions. Singular geometrical perturbations in the form of cavities or inclusions are considered. In the variational context the singular perturbations are replaced by regular perturbations of bilinear forms. The obtained expressions for topological derivatives are useful in numerical method of shape optimization for contact problems as well as in passive control of crack propagation.},
author = {Leugering, Günter and Sokolowski, Jan and Zochowski, Antoni},
booktitle = {Shape- and Topology Optimization for Passive Control of Crack Propagation - New Trends in Shape Optimization},
doi = {10.1007/978-3-319-17563-8{\_}7},
editor = {Aldo Pratelli; Günter Leugering},
faupublication = {yes},
isbn = {978-3-319-17563-8},
keywords = {Frictionless contact;Elastic bodies with cracks;Signorini conditions on cracks;Variational inequality;Shape functional;Shape sensitivity;Topological sensitivity;Domain decomposition;Steklov-Poincare operator;Contact problems},
month = {Jan},
pages = {141-197},
peerreviewed = {unknown},
publisher = {Springer International Publishing},
series = {International Series of Numerical Mathematics},
title = {{Shape}- and {Topology} {Optimization} for {Passive} {Control} of {Crack} {Propagation}},
url = {http://link.springer.com/chapter/10.1007/978-3-319-17563-8{\_}7},
volume = {166},
year = {2015}
}
@article{faucris.107383364,
abstract = {The aim of our work is to develop optimal dielectric composite structures with specific qualities. The task is to design interfaces of given material components such that the originated structure attains certain optical properties. Propagation of the electromagnetic waves in the composite is described by the Helmholtz equation. Success of the structure is enumerated by the objective function which is to be minimized. Interfaces of the given materials are parametrized by the cubic B–spline curves. The design variables are afterwards the positions of B–spline control points. For objective function evaluation one forward computation of the Helmholtz equation is needed. To get the sensitivity of the objective function we solve the backward (adjoint) equation.},
author = {Seifrt, Frantiek and Leugering, Günter and Rohan, Eduard},
doi = {10.1002/pamm.200810705},
faupublication = {yes},
journal = {Proceedings in Applied Mathematics and Mechanics},
pages = {10705-10706},
peerreviewed = {Yes},
title = {{Shape} optimization for the {Helmholtz} equation},
url = {http://onlinelibrary.wiley.com/doi/10.1002/pamm.200810705/full},
volume = {8},
year = {2008}
}
@incollection{faucris.117650104,
abstract = {We consider shape optimization for objects illuminated by light. More precisely, we focus on time-harmonic solutions of the Maxwell system in **curl-curl**-form scattered by an arbitrary shaped rigid object. Given a class of cost functionals, including the scattered energy and the extinction cross section, we develop an adjoint-based shape optimization scheme which is then applied to two key applications.},
author = {Semmler, Johannes and Pflug, Lukas and Stingl, Michael and Leugering, Günter},
booktitle = {New Trends in Shape Optimization},
doi = {10.1007/978-3-319-17563-8{\_}11},
editor = {Aldo Pratelli, Günter Leugering},
faupublication = {yes},
keywords = {Partial Differential Equations; Systems Theory; Control},
pages = {251-269},
peerreviewed = {unknown},
publisher = {Springer},
series = {International Series of Numerical Mathematics},
title = {{Shape} {Optimization} in {Electromagnetic} {Applications}},
volume = {166},
year = {2015}
}
@article{faucris.107373904,
abstract = {The optimization of shape and topology of piezo-patches or layered piezo-electrical material attached to structural parts, such as elastic bodies, plates and shells, plays a major role in the design of smart structures, as piezo-mechanic-acoustic devices in loudspeakers or energy harvesters. While the design for time-harmonic motions is genuinely frequency-dependent, as has been reported in the literature in the context of density optimization with the SIMP-method, time-varying piezoelectric material has not been investigated with respect to the optimal design so far. Therefore, shape sensitivities for layered piezoelectric material and time-varying loads and charges are derived in this paper. In particular, we provide the shape-derivatives for nested piezo-layers associated with a class of shape functional. More general layers can be dealt with similar approach.},
author = {Leugering, Günter and Novotny, A. A. and Perla Menzala, G. and Sokolowski, J.},
doi = {10.1002/mma.1324},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
pages = {2118--2131},
peerreviewed = {Yes},
title = {{Shape} sensitivity analysis of a quasi-electrostatic piezoelectric system in multilayered media},
volume = {33},
year = {2010}
}
@book{faucris.109706124,
abstract = {A review of results on first order shape-topological differentiability of energy functionals for a class of variational inequalities of elliptic type is presented. The velocity method in shape sensitivity analysis for solutions of elliptic unilateral problems is established in the monograph (Sokołowski and Zolésio, Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992). The shape and material derivatives of solutions to frictionless contact problems in solid mechanics are obtained. In this way the shape gradients of the associated integral functionals are derived within the framework of nonsmooth analysis. In the case of the energy type functionals classical differentiability results can be obtained, because the shape differentiability of solutions is not required to obtain the shape gradient of the shape functional (Sokołowski and Zolésio, Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992). Therefore, for cracks the strong continuity of solutions with respect to boundary variations is sufficient in order to obtain first order shape differentiability of the associated energy functional. This simple observation which is used in Sokołowski and Zolésio (Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer, Berlin/Heidelberg/New York, 1992) for the shape differentiability of multiple eigenvalues is further applied in Khludnev and Sokołowski (Eur. J. Appl. Math. 10:379–394, 1999; Eur. J. Mech. A Solids 19:105–120, 2000) to derive the first order shape gradient of the energy functional with respect to perturbations of the crack tip. A domain decomposition technique in shape-topology sensitivity analysis for problems with unilateral constraints on the crack faces (lips) is presented for the shape functionals.We introduce the Griffith shape functional as the distributed shape derivative of the elastic energy evaluated in a domain with a crack, with respect to the crack length. We are interested in the dependence of this functional on domain perturbations far from the crack. As a result, the directional shape and topological derivatives of the nonsmooth Griffith shape functional are obtained with respect to boundary variations of an inclusion.},
author = {Leugering, Günter and Sokolowski, Jan and Zochowski, Antoni},
doi = {10.1007/978-3-319-08025-3{\_}8},
faupublication = {yes},
keywords = {Conical differential of metric projection; Dirichlet Sobolev space; Griffith criterium for crack propagation; Hadamard shape differentiability; Nonsmooth analysis; Shape gradient; Shape Hessian; Signorini variational inequality},
pages = {243-284},
peerreviewed = {Yes},
publisher = {Springer Verlag},
title = {{Shape}-topological differentiability of energy functionals for unilateral problems in domains with cracks and applications},
volume = {101},
year = {2015}
}
@inproceedings{faucris.124195764,
abstract = {We introduce the Griffith shape functional as the distributed shape derivative of the elastic energy evaluated in a domain with a crack, with respect to the crack length. We are interested in the dependence of this functional on domain perturbations far from the crack. As a result, the directional shape and topological derivatives of the nonsmooth Griffith shape functional are obtained with respect to the boundary variations of an inclusion. © 2013 West Pomeranian University of Technology.},
author = {Leugering, Günter and Sokolowski, Jan and Zochowski, Antoni and Sokolowski, Jan and Zochowski, Antoni},
booktitle = {2013 18th International Conference on Methods and Models in Automation and Robotics, MMAR 2013},
faupublication = {yes},
isbn = {9781467355063},
keywords = {energy functional;crack with nonpenetration condition;shape gradient;topological derivative;Griffith's functional},
month = {Jan},
pages = {524-531},
peerreviewed = {Yes},
publisher = {IEEE SERVICE CENTER, 445 HOES LANE, PO BOX 1331, PISCATAWAY, NJ 08855-1331 USA},
title = {{Shape}-topological differentiability of energy functionals in domains with cracks},
url = {https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84893506756&origin=inward},
venue = {Miedzyzdroje},
year = {2013}
}
@article{faucris.122687664,
abstract = {We consider abstract optimal control problems in Banach spaces depending on a small parameter. Problems of this type appear in sensitivity analysis, discretization, perturbation theory and homogenization of heterogenous material. We study the problem of passing to the limit within the framework of variational S-convergence. We derive conditions under which the limiting problems can be made explicit, and we verify such conditions for a number of examples.},
author = {Kogut, Peter I. and Leugering, Günter},
doi = {10.1002/1522-2616(200201)233:1<141::AID-MANA141>3.0.CO;2-I},
faupublication = {no},
journal = {Mathematische Nachrichten},
keywords = {homogenization; S-convergence; optimal control},
month = {Jan},
pages = {141-169},
peerreviewed = {Yes},
title = {{S}-homogenization of optimal control problems in {Banach} spaces},
url = {http://onlinelibrary.wiley.com/doi/10.1002/1522-2616(200201)233:1%3C141::AID-MANA141%3E3.0.CO;2-I/abstract},
volume = {233 - 234},
year = {2002}
}
@article{faucris.214897680,
abstract = {This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks.},
author = {Kufner, Tobias and Leugering, Günter and Semmler, Johannes and Stingl, Michael and Strohmeyer, Christoph},
doi = {10.1051/m2an/2018065},
faupublication = {yes},
journal = {Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique},
note = {CRIS-Team WoS Importer:2019-03-29},
pages = {2409-2431},
peerreviewed = {Yes},
title = {{SIMULATION} {AND} {STRUCTURAL} {OPTIMIZATION} {OF} {3D} {TIMOSHENKO} {BEAM} {NETWORKS} {BASED} {ON} {FULLY} {ANALYTIC} {NETWORK} {SOLUTIONS}},
volume = {52},
year = {2019}
}
@article{faucris.112318844,
abstract = {In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material.Ouraimis toinvestigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations.We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parametersof the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide themanufacturing process ofmaterials with a high fracture toughness.},
author = {Prechtel, Marina and Ronda, Pavel Leiva and Janisch, Rebecca and Hartmaier, Alexander and Leugering, Günter and Steinmann, Paul and Stingl, Michael},
doi = {10.1007/s10704-010-9552-z},
faupublication = {yes},
journal = {International Journal of Fracture},
note = {UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.simula},
peerreviewed = {Yes},
title = {{Simulation} of fracture in heterogeneous elastic materials with cohesive zone models},
year = {2010}
}
@article{faucris.264063015,
abstract = {Singularly perturbed reaction–diffusion equations on a star graph (having k + 1 nodes and k edges) resulting in a system with k individual partial differential equations along the edges with coupling conditions at the common junction are presented. In the singular limit, as the diffusion parameter tends to zero, possibly individually along each edge, boundary layers may occur at the multiple nodes as well as at the simple nodes. Numerically, the proposed equations are solved using central finite difference schemes on properly extended Shishkin meshes. Error estimates are discussed and validated by solving a test problem on a graph with three edges (tripod). A more general graph problem with eight edges and three connecting nodes has also been solved numerically.},
author = {Kumar, Vivek and Leugering, Günter},
doi = {10.1002/mma.7749},
faupublication = {yes},
journal = {Mathematical Methods in the Applied Sciences},
keywords = {central finite difference schemes; k−star graph; networks; Shishkin meshes; tree-like graphs},
note = {CRIS-Team Scopus Importer:2021-09-17},
peerreviewed = {Yes},
title = {{Singularly} perturbed reaction–diffusion problems on a k-star graph},
year = {2021}
}
@article{faucris.222492419,
author = {Meßner, Arthur and Engel, Ulf and Kals, Roland and Vollertsen, Frank},
faupublication = {yes},
journal = {Journal of Materials Processing Technology},
note = {LFT Import::2019-07-16 (1974)},
pages = {371-376},
peerreviewed = {Yes},
title = {{Size} {Effect} in the {FE} {Simulation} of {Micro} {Forming} {Processes}},
volume = {45},
year = {1994}
}
@article{faucris.121559504,
abstract = {We investigate a class of constrained inverse homogenization problems. The complexity of the topological solution is restricted using slope constraint regularization. We show existence of the solution for the inverse optimization problem in function space and outline a converging approximation scheme. We demonstrate how a proper numerical implementation can lead to a stable material design approach. We finally describe results for a comprehensive set of numerical test cases.},
author = {Schury, Fabian and Stingl, Michael and Wein, Fabian},
doi = {10.1007/s00158-012-0795-3},
faupublication = {yes},
journal = {Structural and Multidisciplinary Optimization},
keywords = {Slope constraints;Inverse homogenization;Topology optimization;SIMP},
pages = {813-827},
peerreviewed = {Yes},
title = {{Slope} constrained material design},
volume = {46},
year = {2012}
}
@article{faucris.115874264,
abstract = {For p is not 2, only few results abaout analytic solutions of problems of optimal control of distributed parameter systems with LP-norm have been reported in the literature. In this paper we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. The aim is to steer the system from a position of rest to a constant terminal state in a given finite time. Also more general final configurations are considered.

The objective function that is to be minimized is the maximum of the L-p-norms of the control functions at both boundaries. It is shown that the analytic solution is, in fact, independent of the choice of the p norm that is minimized. So the optimal controls solve a problem of multicriteria optimization, with the L-p-norms as objective functions.},
author = {Gugat, Martin and Leugering, Günter},
faupublication = {yes},
journal = {Computational and Applied Mathematics},
keywords = {optimal control;wave equation;analytic solution;distributed parameter systems;boundary control;robust control; 90C31; 90C34; 49K40},
month = {Jan},
note = {UnivIS-Import:2015-03-09:Pub.2002.nat.dma.lama1.soluti},
pages = {227-244},
peerreviewed = {Yes},
title = {{Solutions} of {L}-p-norm-minimal control problems for the wave equation},
volume = {21},
year = {2002}
}
@article{faucris.111069684,
abstract = {This article presents some calculus rules for contingent epiderivatives of set-valued maps. Among other results the main emphasis is focused on a formula for scalar multiplication, sum formulae and chain rules. The calculus of contingent cones and some inversion theorems are used as a tool. Some applications are also given.},
author = {Jahn, Johannes and Khan, Akhtar Ali},
doi = {10.1080/0233193031000079865},
faupublication = {yes},
journal = {Optimization},
keywords = {Adjacent cone; Chain rule; Clarke's tangent cone; Contingent cone; Contingent epiderivative; Derivability; Optimality conditions; Sum formula},
note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.pama21.someca},
pages = {113-125},
peerreviewed = {Yes},
title = {{Some} {Calculus} {Rules} for {Contingent} {Epiderivatives}},
volume = {52},
year = {2003}
}
@article{faucris.115106024,
abstract = {In this paper several kinds of optima of a vector optimization problem are investigated; these are minimal, weakly minimal, strongly minimal and properly minimal solutions. For these optima various optimality conditions resulting from a scalarization approach are presented. Furthermore some numerical aspects are discussed. © 1985 Springer-Verlag.},
author = {Jahn, Johannes},
doi = {10.1007/BF01719756},
faupublication = {no},
journal = {Or Spectrum},
note = {UnivIS-Import:2015-03-05:Pub.1985.nat.dma.pama21.somech},
pages = {7-17},
peerreviewed = {Yes},
title = {{Some} {Characterizations} of the {Optimal} {Solutions} of a {Vector} {Optimization} {Problem}},
volume = {7},
year = {1985}
}
@inproceedings{faucris.107051164,
abstract = {The problem of exact null controllability of normalized strings and beams subject to boundary controls in an L/sup p/(0,T)-space, where p is larger than or equal to two, is discussed. In particular, the case of L/sup infinity /-controls is of great importance in the applications. It is shown that subtle questions about Fourier series come into play in this problem. In particular, dealing with beam related control problems, lacunary Fourier series play a dominant role; this refers to the notions of (p,q)-sets. Various results on exact controllability with L/sup p/-controls of special string and beam models are given.},
author = {Leugering, Günter},
booktitle = {Decision and Control, 1990., Proceedings of the 29th IEEE Conference},
date = {1990-12-05/1990-12-07},
doi = {10.1109/CDC.1990.203793},
editor = {IEEE},
faupublication = {no},
month = {Jan},
peerreviewed = {unknown},
publisher = {IEEE Xplore},
title = {{SOME} {REMARKS} {ON} {EXACT} {CONTROLLABILITY} {OF} {STRINGS} {AND} {BEAMS} {WITH} {BOUNDARY} {CONTROLS} {IN} {LP}({O},{T}), {P}-{GREATER}-{THAN}-{OR}-{EQUAL}-{TO}-2},
url = {http://ieeexplore.ieee.org/document/203793/},
year = {1990}
}
@misc{faucris.117917184,
author = {Elliot, C and Hintermüller, Michael and Leugering, Günter and Sokolowski, Jan},
doi = {10.1080/10556788.2011.614721},
faupublication = {yes},
month = {Jan},
peerreviewed = {automatic},
title = {{Special} issue on advances in shape and topology optimization: theory, numerics and new applications areas - {Foreword}},
url = {http://www.tandfonline.com/doi/full/10.1080/10556788.2011.614721},
year = {2011}
}
@article{faucris.119291084,
author = {Jahn, Johannes and Chen, G.Y.},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
note = {UnivIS-Import:2015-03-05:Pub.1998.nat.dma.pama21.specia},
pages = {151-285},
peerreviewed = {Yes},
title = {{Special} {Issue} on '{Set}-{Valued} {Optimization}'},
volume = {48},
year = {1998}
}
@article{faucris.110327624,
author = {Jahn, Johannes},
faupublication = {yes},
journal = {Mathematical Methods of Operations Research},
note = {UnivIS-Import:2015-03-05:Pub.1991.nat.dma.pama21.specia},
pages = {175-265},
peerreviewed = {Yes},
title = {{Special} {Issue} on {Vector} {Optimization}},
volume = {35},
year = {1991}
}
@inproceedings{faucris.119852304,
author = {Hante, Falk and Amin, Saurabh and Bayen, Alexandre M.},
booktitle = {Decision and Control, 2008. CDC 2008, 47th IEEE Conference on},
faupublication = {yes},
pages = {2081--2086},
peerreviewed = {unknown},
title = {{Stability} analysis of linear hyperbolic systems with switching parameters and boundary conditions},
year = {2008}
}
@inproceedings{faucris.118588184,
abstract = {We consider the subcritical gas flow through star-shaped pipe networks. The gas flow is modeled by the isothermal Euler equations with friction. We stabilize the isothermal Euler equations locally around a given stationary state on a finite time interval. For the stabilization we apply boundary feedback controls with time-varying delays. The delays are given by C ^{1}-functions with bounded derivatives. In order to analyze the system evolution, we introduce an L ^{2}-Lyapunov function with delay terms. The boundary controls guarantee the exponential decay of the Lyapunov function with time. © 2013 IFIP International Federation for Information Processing.},
address = {Berlin, Heidelberg},
author = {Gugat, Martin and Dick, Markus and Leugering, Günter},
booktitle = {System Modeling and Optimization},
date = {2011-09-12/2011-09-16},
doi = {10.1007/978-3-642-36062-6{\_}26},
faupublication = {yes},
keywords = {boundary feedback stabilization; Euler equations; gas network; Lyapunov function; star-shaped network; time-varying delay},
note = {UnivIS-Import:2015-04-16:Pub.2013.nat.dma.zentr.stabil},
pages = {255-265},
peerreviewed = {Yes},
publisher = {Springer Verlag},
series = {IFIP Advances in Information and Communication Technology},
title = {{Stabilization} of the {Gas} {Flow} in {Star}-{Shaped} {Networks} by {Feedback} {Controls} with {Varying} {Delay}},
url = {http://link.springer.com/chapter/10.1007/978-3-642-36062-6{\_}26},
venue = {Berlin},
volume = {391},
year = {2013}
}
@inproceedings{faucris.118314284,
abstract = {In the application of feedback controls, the computation of the controls may cause a delay. For vibrating systems, a constant delay can destroy the stabilizing effect of the control. To avoid this problem we consider a feedback where a certain delay is a part of the control law and not a perturbation. We consider a string that is fixed at one end and controlled with a boundary feedback with constant delay at the other end. We show the exponential stability of this system that is governed by the wave equation. Moreover, we show the robustness of the stability with respect to variations in time of the feedback parameter that appears as a factor in the control law. ©2010 IEEE.},
author = {Gugat, Martin},
booktitle = {15th International Conference on Methods and Models in Automation and Robotics (MMAR), 2010},
date = {2010-08-23/2010-08-26},
doi = {10.1109/MMAR.2010.5587248},
editor = {IEEE},
faupublication = {yes},
isbn = {978-1-4244-7828-6},
keywords = {asymptotic stability, delays, feedback, vibration control, vibrations, wave equation},
note = {UnivIS-Import:2015-04-16:Pub.2010.nat.dma.zentr.stabil},
pages = {144-147},
peerreviewed = {unknown},
title = {{Stabilizing} a {Vibrating} {String} by {Time} {Delay}},
url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?tp=&arnumber=5587248&queryText%3DGugat%26openedRefinements%3D*%26searchField%3DSearch+All},
venue = {Miedzyzdroje},
year = {2010}
}
@article{faucris.112245584,
abstract = {We consider a star-shaped network consisting of a single node with N ≥ 3 connected arcs. The dynamics on each arc is governed by the wave equation. The arcs are coupled at the node and each arc is controlled at the other end. Without assumptions on the lengths of the arcs, we show that if the feedback control is active at all exterior ends, the system velocity vanishes in finite time. In order to achieve exponential decay to zero of the system velocity, it is not necessary that the system is controlled at all N exterior ends, but stabilization is still possible if, from time to time, one of the feedback controllers breaks down. We give sufficient conditions that guarantee that such a switching feedback stabilization where not all controls are necessarily active at each time is successful. © American Institute of Mathematical Sciences.},
author = {Gugat, Martin and Sigalotti, Mario},
doi = {10.3934/nhm.2010.5.299},
faupublication = {yes},
journal = {Networks and Heterogeneous Media},
keywords = {Feedback stabilization of pdes; Hyperbolic pde; Network; Robustness; Switching control; Switching feedback; Wave equation},
note = {UnivIS-Import:2015-03-09:Pub.2010.nat.dma.zentr.starso},
pages = {299-314},
peerreviewed = {Yes},
title = {{Stars} of vibrating strings: {Switching} boundary feedback stabilization},
url = {http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5215},
volume = {5},
year = {2010}
}
@article{faucris.204141165,
abstract = {We introduce a stationary model for gas flow based on simplified isothermal Euler equations in a non-cycled pipeline network. Especially the problem of the feasibility of a random load vector is analyzed. Feasibility in this context means the existence of a flow vector meeting these loads, which satisfies the physical conservation laws with box constraints for the pressure. An important aspect of the model is the support of compressor stations, which counteract the pressure loss caused by friction in the pipes. The network is assumed to have only one influx node; all other nodes are efflux nodes. With these assumptions the set of feasible loads can be characterized analytically. In addition we show the existence of optimal solutions for some optimization problems with probabilistic constraints. A numerical example based on real data completes this paper.

`shWwWe present the analysis for finding optimal locations and rotations of anisotropic material inclusions in a matrix material by using the polarization matrix. We compare different types of cost functionals, in particular local ones, and show their respective differences. We use the Eshelby theorem and the representation of stresses based on the link matrix. As an analytical model reduction technique, this allows for efficent numerical computation which is demonstrated for two selected examples. `

W

},
author = {Leugering, Günter and Nazarov, Sergei and Schury, Fabian and Stingl, Michael},
doi = {10.1137/110823110},
faupublication = {yes},
journal = {SIAM Journal on Applied Mathematics},
keywords = {asymptotic analysis; Eshelby theorem; optimization; elastic patch; pointwise error estimates; integral and local cost functionals},
pages = {512-534},
peerreviewed = {Yes},
title = {{The} {Eshelby} {Theorem} and {Application} to the optimization of an {Elastic} {Patch}},
volume = {72},
year = {2012}
}
@article{faucris.107390184,
abstract = {We prove the Eshelby theorem for an ellipsoidal piezoelectric inclusion in an infinite piezoelectric material. Explicit formulas for the link and polarization matrices are derived. Passing to the limits with respect to parameters in the corresponding equations, the result is extended to cases when either the inclusion or the surrounding material is purely elastic.},
author = {Leugering, Günter and Nazarov, S. A.},
doi = {10.1007/s00205-014-0803-4},
faupublication = {yes},
journal = {Archive for Rational Mechanics and Analysis},
pages = {n/a},
peerreviewed = {Yes},
title = {{The} {Eshelby} {Theorem} and its {Variants} for {Piezoelectric} {Media}},
year = {2014}
}
@article{faucris.120147544,
abstract = {This short note deals with the issue of existence of contingent epiderivatives for set-valued maps defined from a real normed space to the real line. A theorem of Jahn-Rauh [1], given for the existence of contingent epiderivatives, is used to obtain more general existence results. The strength and the limitations of the main result are discussed by means of some examples.},
author = {Jahn, Johannes and Khan, Akhtar Ali},
doi = {10.1016/S0893-9659(03)90114-5},
faupublication = {yes},
journal = {Applied Mathematics Letters},
keywords = {Contingent cone; Contingent epiderivative; Set-valued maps},
note = {UnivIS-Import:2015-03-09:Pub.2003.nat.dma.pama21.theexi},
pages = {1179-1185},
peerreviewed = {Yes},
title = {{The} {Existence} of {Contingent} {Epiderivatives} for {Set}-{Valued} {Maps}},
volume = {16},
year = {2003}
}
@incollection{faucris.118834364,
address = {Berlin},
author = {Jahn, Johannes},
booktitle = {Multiple Criteria Decision Making, Theory and Application},
editor = {G. Fandel, T. Gal},
faupublication = {no},
note = {UnivIS-Import:2015-04-17:Pub.1980.nat.dma.pama21.thehaa},
pages = {128-134},
peerreviewed = {unknown},
publisher = {Springer},
series = {Lecture Notes in Economics and Mathematical Systems},
title = {{The} {Haar} {Condition} in {Vector} {Optimization}},
volume = {177},
year = {1980}
}
@article{faucris.109406264,
abstract = {The one-dimensional isothermal Euler equations are a well-known model for the flow of gas through a pipe. An essential part of the model is the source term that models the influence of gravity and friction on the flow. In general the solutions of hyperbolic balance laws can blow-up in finite time. We show the existence of initial data with arbitrarily large CL

With respect to the loudspeaker a broad range of objective functions is compared and discussed, culminating in a fully coupled piezoelectric-mechanical-acoustic near field topology optimization problem. Piezoelectric strain cancellation and acoustic short circuits need to be balanced with structural resonance in order to obtain close to resonance performance for almost arbitrary target frequencies. Providing appropriate initial designs proved to be essential for robust optimization.

Cantilevered piezoelectric energy harvesters have been subject to various optimization approaches. However these have generally been based on reduced model assumptions. We present topology optimization of a realistic cantilevered energy harvester model. It proved to be necessary to use advanced topology optimization techniques, stress constraints to enforce practically feasible designs and Heaviside filtering for void features size control and for obtaining a black and white design pattern. To the best of our knowledge, this is the first time that dynamic piezoelectric stress constraints have been formulated for topology optimization. The obtained result is mechanism-based and interpretable to manufacture. This appears to be a novel finding in the field of cantilevered piezoelectric energy harvesting design.

Performing numerical experiments, we were surprised to observe pronounced piezoelectric self-penalization, which means optimal black and white solutions without penalizing design interpolation and additional constraints beside box constraints on the design variable. This phenomenon is only rarely and briefly described in the literature. Within this thesis we perform initial heuristic steps in the analysis of the self-penalization phenomenon, which indeed appears in many different topology optimization problems. Once self-penalization is rigorously understood, our vision is to find methods supporting the self-penalizing effect and to obtain solutions potentially closer to the original problem than constrained and penalized ersatz problems. To this end we present oscillation constraints, a feature size control with independent solid and void feature size without enforcing intermediate pseudo material.

An important point for me is furthermore, that the students will get a picture or a visual impression of mathematical subjects. What does the kernel or the range of a linear mapping mean? What is the difference of an accumulation point an a limit? What does is mean in 2D?

In my presentation I like to present some examples for different mathematical topics like:

- How linear mapping acts on polygon
- Domain and range is not the same
- Sequences in 2d
- Temperature profile in a plate, cylinder and sphere
- Boxplot and dataset

JSXGraph is included in classical HTML-Pages as media content and through dedicated plug-ins for the LMS Moodle and ILIAS. During the “Mathematics for Engineers” (part 1-3) we provide additional material for several topics, e.g. series, (un)-constrained optimization, integration, parametrization of curves and surfaces or differential equations. We see the advantage that the diagrams will become an integral part of the learning modules and the learning unit does not look like patchwork. Further, the learners can focus on the content and do not have to bring additional software or to login in a second learning platform. During presence lectures the lecturer can use the same LMS as the learners do for their follow-up work.

All examples will be published for further usage.

×2 hyperbolic balance laws. The proofs are based on Wave-Front Tracking and therefore we present detailed results on the Riemann problem first.},
address = {Basel},
author = {Gugat, Martin and Herty, Michael and Klar, Axel and Leugering, Günter and Schleper, Veronika},
booktitle = {Constrained Optimization and Optimal Control for Partial Differential Equations},
doi = {10.1007/978-3-0348-0133-1{\_}7},
faupublication = {yes},
isbn = {978-3-0348-0133-1},
keywords = {Hyperbolic conservation laws on networks; optimal control of networked systems; management of fluids in pipelines; 35L65; 49J20},
note = {UnivIS-Import:2015-04-20:Pub.2012.nat.dma.lama1.wellpo},
pages = {123-146},
peerreviewed = {unknown},
publisher = {Springer},
series = {ISNM},
title = {{Well}-posedness of networked hyperbolic systems of balance laws},
url = {http://link.springer.com/chapter/10.1007/978-3-0348-0133-1{\_}7},
volume = {160},
year = {2011}
}
@article{faucris.284143069,
abstract = {We study distributed optimal control problems governed by time-fractional parabolic equations with time dependent coefficients on metric graphs, where the fractional derivative is considered in the Caputo sense. Using the Galerkin method and compactness results, for the spatial part, and approximating the kernel of the time-fractional Caputo derivative by a sequence of more regular kernel functions, we first prove the well-posedness of the system. We then turn to the existence and uniqueness of solutions to the distributed optimal control problem. By means of the Lagrange multiplier method, we develop an adjoint calculus for the right Caputo derivative and derive the corresponding first order optimality system. Moreover, we propose a finite difference scheme to find the approximate solution of the state equation and the resulting optimality system on metric graphs. Finally, examples are provided on two different graphs to illustrate the performance of the proposed difference scheme.},
author = {Mehandiratta, Vaibhav and Mehra, Mani and Leugering, Günter},
doi = {10.1002/asjc.2958},
faupublication = {yes},
journal = {Asian Journal of Control},
note = {CRIS-Team WoS Importer:2022-10-28},
peerreviewed = {Yes},
title = {{Well}-posedness, optimal control and discretization for time-fractional parabolic equations with time-dependent coefficients on metric graphs},
year = {2022}
}
@article{faucris.110283844,
abstract = {In this paper the multiple regression analysis is considered. The regression coefficients obtained by this method are examined with respect to their numerical stability. With simple stability considerations a criteria is given which can be used if an estimator is to evaluate. © 1981 Phydica-Verlag.},
author = {Jahn, Johannes},
doi = {10.1007/BF01902874},
faupublication = {yes},
journal = {Metrika},
note = {UnivIS-Import:2015-03-05:Pub.1981.nat.dma.pama21.zurbew},
pages = {23-33},
peerreviewed = {Yes},
title = {{Zur} {Bewertung} von {Schätzungen} bei der gewöhnlichen {Regressionsanalyse}},
volume = {28},
year = {1981}
}
@incollection{faucris.106876264,
author = {Jahn, Johannes},
booktitle = {Operations Research Verfahren},
faupublication = {no},
note = {UnivIS-Import:2015-03-05:Pub.1979.nat.dma.pama21.zursta},
pages = {209-215},
peerreviewed = {unknown},
title = {{Zur} {Stabilität} von {Regressionskoeffizienten}},
volume = {33},
year = {1979}
}
@article{faucris.121409464,
author = {Jahn, Johannes},
faupublication = {no},
journal = {Optimization},
note = {UnivIS-Import:2015-03-05:Pub.1983.nat.dma.pama21.zurvek},
pages = {577-591},
peerreviewed = {Yes},
title = {{Zur} vektoriellen linearen {Tschebyscheff}-{Approximation}},
volume = {14},
year = {1983}
}