A multiphase shape optimization problem for eigenvalues: Qualitative study and numerical results

Beniamin Bogosel; Bozhidar Velichkov

doi:10.1137/140976406

A multiphase shape optimization problem for eigenvalues: Qualitative study and numerical results

Beniamin Bogosel
, Bozhidar Velichkov

Université Savoie Mont Blanc
Laboratoire Jean Kuntzmann (LJK)

Research output: Contribution to journal › Article › peer-review

Abstract

In thie paper we consider the following multiphase shape optimization problem min {∑_i=1^h λ₁ (Ω_i) + α|Ω_i| : Ω_i open, Ω_i ⊂ D, Ω_i ∩ Ω_j = φ}, where α > 0 is a given constant and D ⊂ ℝ² is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

Original language	English
Pages (from-to)	210-241
Number of pages	32
Journal	SIAM Journal on Numerical Analysis
Volume	54
Issue number	1
DOIs	https://doi.org/10.1137/140976406
Publication status	Published - 1 Jan 2016
Externally published	Yes

Keywords

Eigenvalues
Multiphase
Optimal partition
Shape optimization

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10.1137/140976406

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abstract = "In thie paper we consider the following multiphase shape optimization problem min \{∑i=1h λ1 (Ωi) + α|Ωi| : Ωi open, Ωi ⊂ D, Ωi ∩ Ωj = φ\}, where α > 0 is a given constant and D ⊂ ℝ2 is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.",

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author = "Beniamin Bogosel and Bozhidar Velichkov",

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N2 - In thie paper we consider the following multiphase shape optimization problem min {∑i=1h λ1 (Ωi) + α|Ωi| : Ωi open, Ωi ⊂ D, Ωi ∩ Ωj = φ}, where α > 0 is a given constant and D ⊂ ℝ2 is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

AB - In thie paper we consider the following multiphase shape optimization problem min {∑i=1h λ1 (Ωi) + α|Ωi| : Ωi open, Ωi ⊂ D, Ωi ∩ Ωj = φ}, where α > 0 is a given constant and D ⊂ ℝ2 is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

KW - Eigenvalues

KW - Multiphase

KW - Optimal partition

KW - Shape optimization

U2 - 10.1137/140976406

DO - 10.1137/140976406

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A multiphase shape optimization problem for eigenvalues: Qualitative study and numerical results

Abstract

Keywords

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