A unified approach to shape and topological sensitivity analysis of discretized optimal design problems
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911554372370432 |
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| author | Gangl, Peter Gfrerer, Michael H. |
| author_facet | Gangl, Peter Gfrerer, Michael H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15491 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A unified approach to shape and topological sensitivity analysis of discretized optimal design problems Gangl, Peter Gfrerer, Michael H. Optimization and Control 49Q10, 65K10 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. |
| title | A unified approach to shape and topological sensitivity analysis of discretized optimal design problems |
| topic | Optimization and Control 49Q10, 65K10 |
| url | https://arxiv.org/abs/2209.15491 |