The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions

Abstract

The boundary conditions of an elliptic equation are approximated by using fundamental solutions with singularities located outside the region of interest as trial functions. By letting the singularities change their positions a highly adaptive though nonlinear approximation is achieved employing only a small number of trial functions. The method has been found to work well for problems with boundary data or boundaries of low continuity class. Of particular interest is the ease with which it can be applied to problems in three dimensions.