Method of fundamental solutions

Summary

The method of fundamental solutions approximates the solution of a linear homogeneous elliptic equation by a sum of fundamental solutions. These are centred at source points outside the domain. Each term solves the equation exactly inside the domain, so only the boundary condition has to be fitted. It needs neither a mesh nor integrals, only the evaluation of the fundamental solution at boundary points. It is used when the fundamental solution is known in closed form. Examples are the Laplace equation $\Delta u = 0$, with $\Delta$ the Laplacian, the Helmholtz equation, and linear elasticity. See the definition.