A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems

Gangl P, Gfrerer MH (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Applied Mathematics and Optimization Springer Verlag (Germany)

Book Volume: 88

Article Number: 46

Journal Issue: 2

DOI: 10.1007/s00245-023-10016-2

Abstract

We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is represented by a piecewise linear and globally continuous level set function on a fixed finite element mesh and relate perturbations of the level set function to perturbations of the shape or topology of the corresponding design. We illustrate the sensitivity analysis for a problem that is constrained by a reaction–diffusion equation and draw connections between our discrete sensitivities and the well-established continuous concepts of shape and topological derivatives. Finally, we verify our sensitivities and illustrate their application in a level-set-based design optimization algorithm where no distinction between shape and topological updates has to be made.

Involved external institutions

Johann Radon Institute AT Austria (AT) Technische Universität Graz AT Austria (AT)

How to cite

APA:

Gangl, P., & Gfrerer, M.H. (2023). A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems. Applied Mathematics and Optimization, 88(2). https://dx.doi.org/10.1007/s00245-023-10016-2

MLA:

Gangl, P., and M. H. Gfrerer. "A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems." Applied Mathematics and Optimization 88.2 (2023).

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