Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media

Kaname Matsue, Hisashi Naito

Research output: Contribution to journalArticle

Abstract

In this paper, we study optimization of the first eigenvalue of $$-\nabla \cdot (\rho (x) \nabla u) = \lambda u$$-∇·(ρ(x)∇u)=λu in a bounded domain $$\Omega \subset {\mathbb {R}}^n$$Ω⊂Rn under several constraints for the function $$\rho $$ρ. We consider this problem in various boundary conditions and various topologies of domains. As a result, we numerically observe several common criteria for $$\rho $$ρ for optimizing eigenvalues in terms of corresponding eigenfunctions, which are independent of topology of domains and boundary conditions. Geometric characterizations of optimizers are also numerically observed.

Original languageEnglish
Pages (from-to)489-512
Number of pages24
JournalJapan Journal of Industrial and Applied Mathematics
Volume32
Issue number2
DOIs
Publication statusPublished - Jul 28 2015
Externally publishedYes

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Heat Diffusion
Inhomogeneous Media
First Eigenvalue
Numerical Study
Topology
Boundary conditions
Optimization
Eigenvalues and eigenfunctions
Eigenfunctions
Bounded Domain
Eigenvalue
Subset
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Applied Mathematics

Cite this

Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media. / Matsue, Kaname; Naito, Hisashi.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 32, No. 2, 28.07.2015, p. 489-512.

Research output: Contribution to journalArticle

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