The method of fundamental solutions (MFS) is known to produce remarkable appproximations for some types of boundary data, usually analytic functions and simple boundaries. It is known that in some non favorable situations, the approximation gets worse, even with a better choice of the fictitious sources. On the other hand, the boundary element method (BEM) does not suffer from this limitation, but it leads to large dense matrices to obtain comparable results. In this work, we consider a technique that couples both methods to improve the MFS results, using a less expensive BEM approximation. We present some numerical results to illustrate this.

CEMAT - Center for Computational and Stochastic Mathematics