Work

A probabilistic approach to shape derivatives

Year: 2026

Type: article

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.

Source: Numerische Mathematik

DOI: 10.1007/s00211-026-01554-2

Authors: Luka Schlegel, Volker Schulz, Frank T. Seifried, Maximilian Würschmidt

Institution: Universität Trier

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Universität Trier, Deutsche Forschungsgemeinschaft