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 language | English |
|---|---|
| Pages (from-to) | 489-512 |
| Number of pages | 24 |
| Journal | Japan Journal of Industrial and Applied Mathematics |
| Volume | 32 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jul 28 2015 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media
AU - Matsue, Kaname
AU - Naito, Hisashi
PY - 2015/7/28
Y1 - 2015/7/28
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84938196860&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84938196860&partnerID=8YFLogxK
U2 - 10.1007/s13160-015-0177-5
DO - 10.1007/s13160-015-0177-5
M3 - Article
VL - 32
SP - 489
EP - 512
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
SN - 0916-7005
IS - 2
ER -