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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	210-241
Nombre de pages	32
journal	SIAM Journal on Numerical Analysis
Volume	54
Numéro de publication	1
Les DOIs	https://doi.org/10.1137/140976406
état	Publié - 1 janv. 2016
Modification externe	Oui

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10.1137/140976406

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title = "A multiphase shape optimization problem for eigenvalues: Qualitative study and numerical results",

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.",

keywords = "Eigenvalues, Multiphase, Optimal partition, Shape optimization",

author = "Beniamin Bogosel and Bozhidar Velichkov",

note = "Publisher Copyright: {\textcopyright} 2016 Society for Industrial and Applied Mathematics.",

year = "2016",

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doi = "10.1137/140976406",

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AU - Velichkov, Bozhidar

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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

UR - https://www.scopus.com/pages/publications/84960912697

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 1

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

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