A simple boundary element method for problems of potential in non-homogeneous media

A simple boundary element method for solving potential problems in non-homogeneous media is presented. A physical parameter (e.g. heat conductivity, permeability, permittivity, resistivity, magnetic permeability) has a spatial distribution that varies with one or more co-ordinates. For certain classes of material variations the non-homogeneous problem can be transformed to known homogeneous problems such as those governed by the Laplace, Helmholtz and modified Helmholtz equations. A three-dimensional Galerkin boundary element method implementation is presented for these cases. However, the present development is not restricted to Galerkin schemes and can be readily extended to other boundary integral methods such as standard collocation. A few test examples are given to verify the proposed formulation. The paper is supplemented by an Appendix, which presents an ABAQUS user-subroutine for graded finite elements. The results from the finite element simulations are used for comparison with the present boundary element solutions