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A matrix decomposition MFS algorithm for axisymmetric biharmonic problems

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Abstract

We consider the approximate solution of axisymmetric biharmonic problems using a boundary-type meshless method, the Method of Fundamental Solutions (MFS) with fixed singularities and boundary collocation. For such problems, the coefficient matrix of the linear system defining the approximate solution has a block circulant structure. This structure is exploited to formulate a matrix decomposition method employing fast Fourier transforms for the efficient solution of the system. The results of several numerical examples are presented.

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Authors and Affiliations

  1. Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO, 80401, USA

    Graeme Fairweather

  2. Department of Mathematics and Statistics, University of Cyprus/Πανɛπιστήμι o  Kύπρoυ, P.O. Box 20537, 1678, Nicosia/Λɛυκωσία, Cyprus/Kύπϱoς

    Andreas Karageorghis & Yiorgos-Sokratis Smyrlis

Authors
  1. Graeme Fairweather
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  2. Andreas Karageorghis
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  3. Yiorgos-Sokratis Smyrlis
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Corresponding author

Correspondence to Graeme Fairweather.

Additional information

Communicated by Z. Wu and B.Y.C. Hon

AMS subject classification

65N38, 65F30, 65T50, 65Y99

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Fairweather, G., Karageorghis, A. & Smyrlis, YS. A matrix decomposition MFS algorithm for axisymmetric biharmonic problems. Adv Comput Math 23, 55–71 (2005). https://doi.org/10.1007/s10444-004-1808-6

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  • DOI: https://doi.org/10.1007/s10444-004-1808-6

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