Optimal Partitions for Eigenvalues

نویسندگان

Blaise Bourdin

Dorin Bucur

Édouard Oudet

چکیده

We introduce a new numerical method to approximate 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.

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