Some new results for geometric inverse problems with the method of fundamental solutions

In this paper we solve numerically some geometric inverse problems for linear and semilinear elliptic equations with the method of fundamental solutions (MFS). More precisely, we focus our work on the numerical reconstruction of the unknown domain where the equation holds. We first consider two dimensional problem and we present several numerical experiments with different type of geo metries to be recovered (for example, circular, polygon domains and domains formed by two circular unknown regions). We also present numerical results for three dimensional case. Finally, we analyze semininear equation and then we establish some interesting open problems related to the subject.