Numerical Algorithms

, Volume 72, Issue 1, pp 107–130 | Cite as

On choosing the location of the sources in the MFS

Original Paper

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.

Keywords

Method of fundamental solutions Laplace equation Biharmonic equation Non-harmonic boundary conditions 

Mathematics Subject Classification (2010)

Primary 65N35 Secondary 65N38 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.College of MathematicsTaiyuan University of TechnologyShanxiChina
  2. 2.Department of MathematicsUniversity of Southern MississippiHattiesburgUSA
  3. 3.Department of Mathematics and StatisticsUniversity of CyprusNicosiaCyprus

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