Non-homogeneous field potential problems solution by the modified local Green's function method (MLGFM)

Abstract A question in the boundary element method procedures which has not received a satisfactory answer up until now is the treatment of problems in media where the properties change continuously or piecewise continuously. In such cases, there are no known fundamental solutions. This paper describes an attempt for solving these problems and is based on the modified local Green's function method which does not require the knowledge of the explicit form of a fundamental solution. Presently, this method is reviewed in its simplest form and it is also shown to be related to the Galerkin boundary element method. Some numerical results for non-homogeneous potential problems are presented.