OPTIMAL PARTITIONS FOR EIGENVALUES

被引：38

作者：

Bourdin, Blaise ^{[1
]}

Bucur, Dorin ^{[2
]}

Oudet, Edouard ^{[2
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Univ Savoie, Lab Math LAMA, UMR 5127, F-73376 Le Bourget Du Lac, France

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2009年 / 31卷 / 06期

基金：

美国国家科学基金会;

关键词：

gamma-convergence; shape analysis;

D O I：

10.1137/090747087

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：4100 / 4114

页数：15

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