A localization technique is proposed to solve some elliptic problems based on the classical Schwarz overlapping method. The original problem is converted to solving a sequence of subproblems (which are much less than the original problem) resulting in an iterative method. The local problems are solved by the Method of Fundamental Solutions. The localization technique makes it possible to apply the method to inhomogeneous problems and to more general problems as well. The method can be embedded into a natural multi-level context, which significantly improves the computational efficiency. As a further application, the proposed method is applied to the scattered data interpolation problem.