Optimal Partitions for Eigenvalues
Blaise Bourdin, Dorin Bucur, Édouard Oudet · SIAM Journal on Scientific Computing · 2009
We introduce a new numerical method for approximating partitions of a domain minimizing the sum of Dirichlet–Laplacian eigenvalues of any order. First we prove the equivalence of the original problem and a relaxed formulation based on measures. Using this result, we build a numerical algorithm to approximate optimal configurations. We describe numerical experiments aimed at studying the asymptotic behavior of optimal partitions with large numbers of cells.