MATHEMATICAL IMPLEMENTATION OF BOUNDARY ELEMENT METHOD

Abstract

The Boundary Element Method is defined as type of a numerical method that approximates solutions of boundary value problems. The most important aspect in which the Boundary Element Method distinguishes itself from other numerical methods is the fact that only the boundary of a domain needs to be discretized. In many other numerical methods, such as the finite element method, finite differences or the finite volume method, in addition to the boundary, the interior of the domain also needs to be discretized. As a consequence of the boundary discretization, the Boundary Element Method is a suitable method for problems on external domains, or domains that have a free or moving boundary. Also problems in which singularities or discontinuities occur can be handled efficiently by the Boundary Element Method. Another advantage of the Boundary Element Method is that variables and their derivatives, for instance temperature and its flux, are computed with the same degree of accuracy.