Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

Abstract

The method of fundamental solutions (MFS) is a Trefftz-type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo-boundary, i.e., a surface embracing the domain of the problem under consideration. In this work, we develop a mathematical framework for the numerical implementation of the MFS in elliptic systems. We obtain density results, with respect to the C ℓ-norms, which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo-elastostatics. The domains in our density results may possess holes and they satisfy the segment condition. © 2008 Springer-Verlag.