BEM treatment of three-dimensional anisotropic field problems by direct domain mapping

In this paper, the method of characteristics which has been employed to reduce two-dimensional steady-state anisotropic field problems to ones governed by the simple Laplace equation in a mapped domain, is extended to numerically treat similar three-dimensional problems by the boundary element method (BEM). The proposed process does not involve any rotation of coordinate axes as is normally done in the literature. The advantage of this approach is that the three-dimensional anisotropic field problem can then be easily solved with any readily available BEM programs for three-dimensional 'isotropic' potential theory. The validity of the proposed scheme is demonstrated by three numerical examples where the results are compared with those obtained using the finite element method with the commercial code ANSYS.