Open Access

ARTICLE

A Regularized Method of Fundamental Solutions Without Desingularization

C. Gáspár¹

1 Széchenyi István University, Gyõr, Hungary

Computer Modeling in Engineering & Sciences 2013, 92(1), 103-121. https://doi.org/10.3970/cmes.2013.092.103

Abstract

Some regularized versions of the Method of Fundamental Solutions are investigated. The problem of singularity of the applied method is circumvented in various ways using truncated or modified fundamental solutions, or higher order fundamental solutions which are continuous at the origin. For pure Dirichlet problems, these techniques seem to be applicable without special additional tools. In the presence of Neumann boundary condition, however, they need some desingularization techniques to eliminate the appearing strong singularity. Using fundamental solutions concentrated to lines instead of points, the desingularization can be omitted. The method is illustrated via numerical examples.

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Keywords

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