Solution of Inverse Geometric Problems Using a Non-Iterative MFS

In most of the method of fundamental solutions (MFS) approaches employed so far for the solution of inverse geometric problems, the MFS implementation typically leads to non-linear systems which were solved by standard nonlinear iterative least squares software. In the current approach, we apply a three-step non- iterative MFS technique for identifying a rigid inclusion from internal data measurements, which consists of: (i) a direct problem to calculate the solution at the set of measurement points, (ii) the solution of an ill-posed linear problem to determine the solution on a known virtual boundary and (iii) the solution of a direct problem in the virtual domain which leads to the identification of the unknown curve using the MATLAB (R) functions contour in 2D and isosurface in 3D. The results of several numerical experiments for steady-state heat conduction and linear elasticity in two and three dimensions are presented and analyzed.