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On choosing the location of the sources in the MFS

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Abstract

The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions (MFS). In this work we investigate this issue by means of two algorithms, one based on the satisfaction of the boundary conditions and one based on the leave-one-out cross validation algorithm. By applying these algorithms to several numerical examples for the Laplace and biharmonic equations in a variety of geometries in two and three dimensions, we obtain locations of the sources which lead to highly accurate results, at a relatively low cost.

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Shanxi, China

    C. S. Chen & Yan Li

  2. Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS, 39406, USA

    C. S. Chen

  3. Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678, Nicosia, Cyprus

    A. Karageorghis

Authors
  1. C. S. Chen
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  2. A. Karageorghis
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  3. Yan Li
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Correspondence to A. Karageorghis.

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Chen, C.S., Karageorghis, A. & Li, Y. On choosing the location of the sources in the MFS. Numer Algor 72, 107–130 (2016). https://doi.org/10.1007/s11075-015-0036-0

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  • DOI: https://doi.org/10.1007/s11075-015-0036-0

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