{"title":"Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli","authors":"C.S. Chen,Andreas Karageorghis, Min Lei","doi":"10.4208/nmtma.oa-2023-0045","DOIUrl":null,"url":null,"abstract":"We apply the local method of fundamental solutions (LMFS) to boundary\nvalue problems (BVPs) for the Laplace and homogeneous biharmonic equations in\nannuli. By appropriately choosing the collocation points, the LMFS discretization\nyields sparse block circulant system matrices. As a result, matrix decomposition\nalgorithms (MDAs) and fast Fourier transforms (FFTs) can be used for the solution\nof the systems resulting in considerable savings in both computational time and\nstorage requirements. The accuracy of the method and its ability to solve large scale\nproblems are demonstrated by applying it to several numerical experiments.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"80 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Mathematics-Theory Methods and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/nmtma.oa-2023-0045","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.
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