Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives
The author considers a shape optimization issue for an eigenvalue Dirichlet boundary value problem attached to the Laplace equation. For this problem, a standard Ritz-Galerkin f. e. m. approximation along with its weak variational formulation are used during shape evolution. Then the author analyses two cases, a geometry constrained one and another unconstrained. Both are solved by two shape gradient descent algorithms based on shape sensitive analysis. Some interesting numerical experiments are carried out.
scientific article; zbMATH DE number 6852045
scientific article