Computing extremal eigenvalues for three-dimensional photonic crystals with wave vectors near the Brillouin zone center
type: Item
instance of: scholarly article
title: Computing extremal eigenvalues for three-dimensional photonic crystals with wave vectors near the Brillouin zone center
zbMATH Open document ID: 1271.65065
author: Tsung-Ming Huang
author: Yueh-Cheng Kuo
author: Weichung Wang
published in: Journal of Scientific Computing
publication date: 2013-06-19T00:00:00Z
full work available at URL: index.html
review text: The authors consider a matrix eigenvalue problem \(Ax=\lambda Bx\) with \(A\) positive semi-definite and \(B\) positive definite and diagonal, arising in the finite difference solution of Maxwell's equations. The problem studied arises in the study of wave vectors close to the centre of the Brillouin zone of a cubic photonic crystal (a periodic dielectric medium). This problem has many zero eigenvalues, a couple of very small non-zero eigenvalues, and several much larger eigenvalues. The authors determine the number of zero eigenvalues and analyze the structure of the null spaces. They compare two methods (the hybrid Jacobi-Davidson method and the shift-and-invert Krylov-Schur method) for computing the small non-zero eigenvalues, and numerically test how performance is affected by the choice of shift values, condition numbers, and initial vectors.
reviewed by: Alan L. Andrew
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 35Q61
Mathematics Subject Classification ID: 78M20
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6176968
zbMATH Keywords: Brillouin zone center
zbMATH Keywords: matrix eigenvalue problems
zbMATH Keywords: preconditioners
zbMATH Keywords: Krylov-Schur method
zbMATH Keywords: Jacobi-Davidson method
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: three-dimensional photonic crystals
zbMATH Keywords: finite difference
zbMATH Keywords: wave vectors
zbMATH Keywords: condition numbers
describes a project that uses: TRLan
describes a project that uses: SLEPc
describes a project that uses: JDQR
describes a project that uses: JDQZ
MaRDI profile type: Publication
OpenAlex ID: W2013469044
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DOI: 10.1007/S10915-012-9646-Z
description: scientific article; zbMATH DE number 6176968