The method of fundamental solutions for Helmholtz-type problems

The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated
with two- or three-dimensional Helmholtz-type equations. Inverse problems have become more and more important in various fields of sicence and technology, and
have certainly been one of the fastest growing areas in applied mathematics over the last three decades. However, as inverse geometric problems typically lead to
mathematical models which are ill-posed, their solutions are unstable under data perturbations and classical numerical techniques fail to provide accurate and stable
solutions.