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. © 2009 Society for Industrial and Applied Mathematics.
Publication Source (Journal or Book title)
SIAM Journal on Scientific Computing
Bourdin, B., Bucur, D., & Oudet, É. (2009). Optimal partitions for eigenvalues. SIAM Journal on Scientific Computing, 31 (6), 4100-4114. https://doi.org/10.1137/090747087