A Robust Numerical Algorithm for Computing Maxwell's Transmission Eigenvalue Problems

DOI10.1137/15M1018927zbMath1408.78005OpenAlexW1772520964MaRDI QIDQ3447467

Wei-Qiang Huang, Tsung-Ming Huang, Wen-Wei Lin

Publication date: 27 October 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1018927

zbMATH Keywords

Maxwell's equationsquadratic eigenvalue problemstransmission eigenvaluesLOBPCGsecant-type iteration

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Preconditioners for iterative methods (65F08)

Related Items

Efficient methods of computing interior transmission eigenvalues for the elastic waves, A spectral projection method for transmission eigenvalues, On the transmission eigenvalue problem for the acoustic equation with a negative index of refraction and a practical numerical reconstruction method, A Holomorphic Operator Function Approach for the Transmission Eigenvalue Problem of Elastic Waves, Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method, An efficient spectral-Galerkin approximation and error analysis for Maxwell transmission eigenvalue problems in spherical geometries, A Lowest-Order Mixed Finite Element Method for the Elastic Transmission Eigenvalue Problem, A Simple Low-Degree Optimal Finite Element Scheme for the Elastic Transmission Eigenvalue Problem, A lowest-order virtual element method for the Helmholtz transmission eigenvalue problem, A C\(^{0}\)IP method of transmission eigenvalues for elastic waves

Uses Software

• Algorithm 922
• lobpcg.m

Cites Work

• Unnamed Item
• Unnamed Item
• An indefinite variant of LOBPCG for definite matrix pencils
• A multigrid method for Helmholtz transmission eigenvalue problems
• On spectral analysis and a novel algorithm for transmission eigenvalue problems
• A coupled BEM and FEM for the interior transmission problem in acoustics
• On the determination of Dirichlet or transmission eigenvalues from far field data
• The interior transmission problem
• Mixed finite elements in \(\mathbb{R}^3\)
• Trace minimization principles for positive semi-definite pencils
• Eigenvalue solvers for three dimensional photonic crystals with face-centered cubic lattice
• On the existence of transmission eigenvalues
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• Finite Element Methods for Maxwell's Transmission Eigenvalues
• Algorithm 922
• Estimation of transmission eigenvalues and the index of refraction from Cauchy data
• The Existence of an Infinite Discrete Set of Transmission Eigenvalues
• Iterative Methods for Transmission Eigenvalues
• The interior transmission problem for anisotropic Maxwell's equations and its applications to the inverse problem
• On the use of transmission eigenvalues to estimate the index of refraction from far field data
• A Null Space Free Jacobi--Davidson Iteration for Maxwell's Operator
• Transmission eigenvalues and the nondestructive testing of dielectrics
• Analytical and computational methods for transmission eigenvalues
• The inverse electromagnetic scattering problem for anisotropic media
• Transmission Eigenvalues
• Finite Element Methods for Maxwell's Equations
• On the existence of transmission eigenvalues in an inhomogeneous medium
• Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence
• A numerical method to compute interior transmission eigenvalues
• Computation of Maxwell’s transmission eigenvalues and its applications in inverse medium problems
• Inverse acoustic and electromagnetic scattering theory