Optimal sources in the MFS by minimizing a new merit function: Energy gap functional

The accuracy of the method of fundamental solutions (MFS) is strongly dependent on the distribution of source points. A proper choice of source points is still an important issue in the MFS. In this paper we derive a new merit function, namely the energy gap functional, whose minimum leads to the optimal distribution of source points. The new method can improve the accuracy of the MFS for solving the mixed boundary value problem as well as the Cauchy problem of the Laplace equation. The numerical tests confirm that the use of the optimal sources in the MFS performs well and the accuracy is increased.