On the Spectrum of an Operator Pencil with Applications to Wave Propagation in Periodic and Frequency Dependent Materials

DOI10.1137/080728779zbMath1191.47059arXiv0803.0456OpenAlexW1987938208MaRDI QIDQ5189584

Publication date: 17 March 2010

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

Full work available at URL: https://arxiv.org/abs/0803.0456

zbMATH Keywords

periodic structure operator pencil quadratic eigenvalue band-gap Bloch wave gyroscopic

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) General theory of partial differential operators (47F05) Electromagnetic theory (general) (78A25) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Matrix pencils (15A22)

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A pseudospectral mapping theorem for operator pencils ⋮ ON THE SPECTRUM OF A HOLOMORPHIC OPERATOR-VALUED FUNCTION WITH APPLICATIONS TO ABSORPTIVE PHOTONIC CRYSTALS ⋮ Numerical realization of Dirichlet-to-Neumann transparent boundary conditions for photonic crystal wave-guides ⋮ Structure-preserving methods for computing complex band structures of three dimensional photonic crystals ⋮ A multiscale \(hp\)-FEM for 2D photonic crystal bands ⋮ \((n,\varepsilon)\)-condition spectrum of operator pencils ⋮ A Gutzwiller trace formula for stationary space-times ⋮ Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations ⋮ Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications ⋮ Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients ⋮ New sufficient conditions for the computation of generalized eigenvalues ⋮ Complex dispersion relation calculations with the symmetric interior penalty method ⋮ Singular Value Decompositions for Single-Curl Operators in Three-Dimensional Maxwell's Equations for Complex Media

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