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Volume 17, Issue 1
Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli

C.S. Chen, Andreas Karageorghis & Min Lei

DOI: 10.4208/nmtma.OA-2023-0045

Numer. Math. Theor. Meth. Appl., 17 (2024), pp. 93-120.

Published online: 2024-02

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  • 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.

  • Keywords

Local method of fundamental solutions, Poisson equation, biharmonic equation, matrix decomposition algorithms, fast Fourier transforms.

  • AMS Subject Headings

Primary 65N35, Secondary 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-17-93, author = {Chen , C.S.Karageorghis , Andreas and Lei , Min}, title = {Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0045}, url = {http://global-sci.org/intro/article_detail/nmtma/22912.html} }
TY - JOUR T1 - Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli AU - Chen , C.S. AU - Karageorghis , Andreas AU - Lei , Min JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 93 EP - 120 PY - 2024 DA - 2024/02 SN - 17 DO - http://doi.org/10.4208/nmtma.OA-2023-0045 UR - https://global-sci.org/intro/article_detail/nmtma/22912.html KW - Local method of fundamental solutions, Poisson equation, biharmonic equation, matrix decomposition algorithms, fast Fourier transforms. AB -

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.

Chen , C.S.Karageorghis , Andreas and Lei , Min. (2024). Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli. Numerical Mathematics: Theory, Methods and Applications. 17 (1). 93-120. doi:10.4208/nmtma.OA-2023-0045
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