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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.15967 |
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| _version_ | 1866908786924453888 |
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| author | Schlegel, Luka Schulz, Volker Seifried, Frank T. Würschmidt, Maximilian |
| author_facet | Schlegel, Luka Schulz, Volker Seifried, Frank T. Würschmidt, Maximilian |
| contents | We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for second-order semilinear elliptic PDEs with Dirichlet boundary conditions and a general class of target functions. The probabilistic representation derives from an extension of a boundary sensitivity result for diffusion processes due to Costantini, Gobet and El Karoui [14]. Moreover, we present a simulation methodology based on our results that does not necessarily require a mesh of the relevant domain, and provide Taylor tests to verify its numerical accuracy |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Probabilistic Approach to Shape Derivatives Schlegel, Luka Schulz, Volker Seifried, Frank T. Würschmidt, Maximilian Optimization and Control Probability We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for second-order semilinear elliptic PDEs with Dirichlet boundary conditions and a general class of target functions. The probabilistic representation derives from an extension of a boundary sensitivity result for diffusion processes due to Costantini, Gobet and El Karoui [14]. Moreover, we present a simulation methodology based on our results that does not necessarily require a mesh of the relevant domain, and provide Taylor tests to verify its numerical accuracy |
| title | A Probabilistic Approach to Shape Derivatives |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2409.15967 |