Rational eigenvalue problems and applications to photonic crystals

DOI10.1016/j.jmaa.2016.07.048zbMath1351.65084arXiv1507.06381OpenAlexW2492967703MaRDI QIDQ323799

Christiane Tretter, Christian Engström, Heinz K. Langer

Publication date: 10 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.06381

zbMATH Keywords

eigenvaluefinite element methodvariational principlespectral gaptwo-sided boundsphotonic crystalmulti-pole Lorentz modelsnon-linear spectral problem

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Statistical mechanics of crystals (82D25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (14)

Pseudo numerical ranges and spectral enclosures ⋮ A subspace iteration algorithm for Fredholm valued functions ⋮ Finite element calculation of photonic band structures for frequency dependent materials ⋮ Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures ⋮ Enclosure of the numerical range of a class of non-selfadjoint rational operator functions ⋮ Enclosure of the numerical range and resolvent estimates of non-selfadjoint operator functions ⋮ On equivalence and linearization of operator matrix functions with unbounded entries ⋮ Physically agnostic quasi normal mode expansion in time dispersive structures: from mechanical vibrations to nanophotonic resonances ⋮ Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory ⋮ Mathematical and Numerical Analysis of the Generalized Complex-Frequency Eigenvalue Problem for Two-Dimensional Optical Microcavities ⋮ Spectral analysis of polygonal cavities containing a negative-index material ⋮ Accumulation of complex eigenvalues of a class of analytic operator functions ⋮ Spectral approximation for polynomial eigenvalue problems ⋮ Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation

Uses Software

• Concepts

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