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An operator method for a numerical quadrature finite element method for a Maxwell‐eigenvalue problem
Author(s) -
Hamelinck Wouter,
Van Keer Roger
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.868
Subject(s) - mathematics , spurious relationship , eigenvalues and eigenvectors , gauss–kronrod quadrature formula , quadrature (astronomy) , finite element method , gaussian quadrature , numerical integration , numerical analysis , tanh sinh quadrature , operator (biology) , gauss–jacobi quadrature , mathematical analysis , clenshaw–curtis quadrature , nyström method , integral equation , physics , biochemistry , statistics , quantum mechanics , gene , transcription factor , optics , chemistry , repressor , thermodynamics
We consider a Maxwell‐eigenvalue problem on a brick. As is well known, we need to pay special attention to avoiding the so‐called spurious eigenmodes. We extend the results obtained in ( SIAM J. Numer. Anal. 2000; 38 :580–607) to include the use of numerical quadrature. For simplicity, we restrict ourselves to a Gauss–Lobatto integration scheme. The numerical quadrature variational problem can be recasted in an operator form. The main goal of the article consists of proving that a set of necessary and sufficient conditions for spurious freeness remain valid while using numerical quadrature with sufficient precision. Copyright © 2007 John Wiley & Sons, Ltd.