A level set method for Laplacian eigenvalue optimization subject to geometric constraints

• Published in: Computational optimization and applications Vol. 82; no. 2; pp. 499 - 524
• Main Authors: Qian, Meizhi, Zhu, Shengfeng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Algorithms; Convex and Discrete Geometry; Dirichlet problem; Eigenvalues; Finite element method; Geometric constraints; Management Science; Mathematical analysis; Mathematics; Mathematics and Statistics; Operations Research; Operations Research/Decision Theory; Optimization; Shape optimization; Statistics; Eigenvalue optimization; Eulerian derivative; Relaxed approach; Level set method; Finite element

We consider to solve numerically the shape optimization problems of Dirichlet Laplace eigenvalues subject to volume and perimeter constraints. By combining a level set method with the relaxation approach, the algorithm can perform shape and topological changes on a fixed grid. We use the volume expr...