1. A Probabilistic Approach to Shape Derivatives
- Author
-
Schlegel, Luka, Schulz, Volker, Seifried, Frank T., and Würschmidt, Maximilian
- Subjects
Mathematics - Optimization and Control ,Mathematics - Probability - Abstract
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
- Published
- 2024