In the present work, we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems. More specifically, we study whether linear combinations of fundamental solutions can approximate the solutions of the boundary value problems under consideration. In our study, the singularities ...

The method of fundamental solutions (also known as the singularity or the source method) is a useful technique for solving linear partial di erential equations such as the Laplace or the Helmholtz equation. The procedure involves only boundary collocation or boundary tting and hence is a very fast procedure for the solution of these classes of problems. The resulting coe cient matrix, is howeve...

We consider the application of the method of fundamental solutions to isotropic elastostatics problems in three space dimensions. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy–Navier equations of elasticity, which are expressed in terms of sources placed outside the domain of the problem under consideration. The final positions of the sourc...

This paper describes the applications of the method of fundamental solutions (MFS) as a mesh-free numerical method for the Stokes’ first and second problems which prevail in the semi-infinite domain with constant and oscillatory velocity at the boundary in the fluid-mechanics benchmark problems. The time-dependent fundamental solutions for the semi-infinite problems are used directly to obtain ...

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation p...