Optimal Localization of Eigenfunctions in an Inhomogeneous Medium

DOI10.1137/S0036139903426162zbMath1060.65068OpenAlexW2041221658MaRDI QIDQ4830559

David C. Dobson, Fadil Santosa

Publication date: 13 December 2004

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036139903426162

zbMATH Keywords

numerical experimentsfinite difference schemeelectromagnetic waveseigenfunctionmultiple eigenvaluemode localizationoptimal designspectral problemoptical devicesDirichlet eigenvalue problemsteepest descent methodminimization methodband gap phenomenon

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods based on necessary conditions (49M05) General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for second-order elliptic equations (35J20) Methods of reduced gradient type (90C52) Physical optics (78A10) Optimization problems in optics and electromagnetic theory (78M50)

Related Items (5)

Optimization of spectral functions of Dirichlet-Laplacian eigenvalues ⋮ Optimization of scattering resonances ⋮ Reduced basis approximation anda posteriorierror estimates for parametrized elliptic eigenvalue problems ⋮ Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression ⋮ Maximization of the quality factor of an optical resonator

Uses Software

• Matlab

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