On the choice of optimal source points in MFS by an energy method for 3D Laplace operator

By using the method of fundamental solutions (MFS) for solving direct/inverse boundary value problems in a bounded domain, the existing inequality in the energy gap functional (EGF) leads to the choice of optimal source points which can be improve the accuracy of the MFS. In this paper, the mentioned method is implemented for solving inverse Cauchy problems involving 3D Laplace operator. The simplicity and efficiency of this method can be confirmed in several numerical tests.