Methods of fundamental solutions for harmonic and biharmonic boundary value problems

Abstract

In this work, the use of the Method of Fundamental Solutions (MFS) for solving elliptic partial differential equations is investigated, and the performance of various least squares routines used for the solution of the resulting minimization problem is studied. Two modified versions of the MFS for harmonic and biharmonic problems with boundary singularities, which are based on the direct subtraction of the leading terms of the singular local solution from the original mathematical problem, are also examined. Both modified methods give more accurate results than the standard MFS and also yield the values of the leading singular coefficients. Moreover, one of them predicts the form of the leading singular term.