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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 184786, 15 pages
http://dx.doi.org/10.1155/2015/184786
Research Article

A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains

Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

Received 2 July 2015; Accepted 25 October 2015

Academic Editor: Salvatore Alfonzetti

Copyright © 2015 Oscar P. Bruno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new computational method for the solution of elliptic eigenvalue problems with variable coefficients in general two-dimensional domains. The proposed approach is based on use of the novel Fourier continuation method (which enables fast and highly accurate Fourier approximation of nonperiodic functions in equispaced grids without the limitations arising from the Gibbs phenomenon) in conjunction with an overlapping patch domain decomposition strategy and Arnoldi iteration. A variety of examples demonstrate the versatility, accuracy, and generality of the proposed methodology.