ABSTRACT
Boundary element methods (BEMs) constitute a recent development in computational mathematics for the solution of boundary value problems in various branches of science and technology. These methods evolved from integral equation methods which are known as boundary integral equation methods (BIEMs). There were, in fact, two types of BIEM's which, though seemingly alike, had totally different approaches of formulation. The BEM is based on integral equation formulation of boundary value problems and requires discretization of only the boundary (surface or curve) and not the interior of the region under consideration. The 'direct' BEM which is presented and pursued is based on the Galerkin–type weak variational formulation where the discretized boundary element equations are formulated with the help of the fundamental solutions of the related field equations. A practical comparison of the BEM with the finite element method can be made on the basis of numerical and computational criteria.
