O Método das Soluções Fundamentais com Expansão em Multipolos

Abstract

In this work we present an implementation of Method Fundamental Solutions (MFS) combined with the method of Fast Multipole (FMM) which we call the MFS-FMM. Some numerical experiments were performed considering a Laplace problem de ned in a two-dimensional domain, where the algorithm presented accurately compatible with that obtained through the classic MFS. We highlight two advantages of the solution given by the algorithm on the MFS: 1) lower computational cost and 2) the resulting linear system proved to be well conditioned, the in contrest of what happens to the MFS that needs to be regularized. In particular, this second feature is and quite relevant in the presence of data with noise, as in the case of inverse problems, where MFS has played a prominent role in many applications.