Year: 2024
Author: C.S. Chen, Andreas Karageorghis, Min Lei
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 1 : pp. 93–120
Abstract
We apply the local method of fundamental solutions (LMFS) to boundary value problems (BVPs) for the Laplace and homogeneous biharmonic equations in annuli. By appropriately choosing the collocation points, the LMFS discretization yields sparse block circulant system matrices. As a result, matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs) can be used for the solution of the systems resulting in considerable savings in both computational time and storage requirements. The accuracy of the method and its ability to solve large scale problems are demonstrated by applying it to several numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0045
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 1 : pp. 93–120
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Local method of fundamental solutions Poisson equation biharmonic equation matrix decomposition algorithms fast Fourier transforms.