Gangl P, Gfrerer MH (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 88
Article Number: 46
Journal Issue: 2
DOI: 10.1007/s00245-023-10016-2
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.
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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