Bundling Efforts – How to offer quizzes as a service for lecturers - Bird, Anja; Hild, Johannes (Computer Aided Assessment and Feedback in Mathematics: Contributions to the 3rd International STACK conference 2020, 2020)

Numerische Verfahren für optimalen Massentransport in der Registrierung medizinischer Bilddaten - Hild, Johannes (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2007)
In der vorliegenden Arbeit werden zwei numerische Verfahren für die Registrierung medizinischer Bilddaten vorgestellt. Beide Verfahren beruhen auf der numerischen Lösung eines Optimierungsproblems, welches eine Transportgleichung als Nebenbedingung besitzt. Der Lösungsalgorithmus koppelt ein Innere-Punkte-Verfahren für das Optimierungsproblem mit einem Finite-Elemente-Verfahren für die Transportgleichung.

Optimale Steuerung von Flachwasserkanälen - Rathmann, Wigand; Hild, Johannes (Proceedings 14. Workshop Mathematik in ingenieurwissenschaftlichen Studiengängen, 2017)

Performance and Comparison of BlueM.MPC and Lamatto - Heusch, Steffen; Hild, Johannes; Leugering, Günter; Ostrowski, Manfred (Mathematical Optimization of Water Networks, 2012)
We compare the quality and generation performance of the optimal control sequence produced by the software frameworks BlueM.MPC and Lamatto.

Real-Time Control of Hydrodynamic Process Models on Finite Volume Networks - Hild, Johannes (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2012)
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.

Real-Time Control of Urban Drainage Systems - Hild, Johannes; Leugering, Günter (Mathematical Optimization of Water Networks, 2012)
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.