A Fourier Continuation Method for the Solution of Elliptic Eigenvalue Problems in General Domains
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.
© 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. Received 2 July 2015; Accepted 25 October 2015. The authors declare that there is no conflict of interests regarding the publication of this paper. The authors gratefully acknowledge support from NSF and AFOSR.
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