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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.
Original language | English |
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Article number | 46 |
Journal | Applied Mathematics & Optimization |
Volume | 88 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- Design optimization
- Finite element method
- Shape derivative
- Topological derivative
- Unified sensitivity analysis
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics
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A unified approach to shape and topological sensitivity analysis of discretized optimal design problems
Gfrerer, M. H. (Speaker)
9 May 2023Activity: Talk or presentation › Invited talk › Science to science