03.06.2024 15:00 Maximilian Würschmidt (Universität Trier):
A Probabilistic Approach to Shape Derivatives B 349 (Theresienstr. 39, 80333 München)
In this talk, 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 a boundary sensitivity result for diffusion processes due to Costantini, Gobet and El Karoui. Via so-called Taylor tests we verify the numerical accuracy of our methodology.