Year: 2007
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 169–184
Abstract
We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse iteration method. The problem is formulated as a generalized eigenvalue problems. By modifying the exact inverse iteration algorithm for the eigenvalue problem, we design a new adaptive inverse iteration finite element algorithm. Adaptive finite element methods based on a posteriori error estimate are known to be successful in resolving singularities of eigenfunctions which deteriorate the finite element convergence. We construct a posteriori error estimator for the electromagnetic guided waves problem. Numerical results are reported to illustrate the quasi-optimal performance of our adaptive inverse iteration finite element method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-JCM-8683
Journal of Computational Mathematics, Vol. 25 (2007), Iss. 2 : pp. 169–184
Published online: 2007-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Waveguides Eigenvalue Problem Inverse Iteration Algorithm Adaptive Finite Element Method.