Un Análisis del Método de los Elementos de Contorno

Abstract

In some engineering problems it is required to find numerical solutions of Poisson differential equation in a restricted number of points. In these situations the Boundary Element Method (BEM) seems advantageous with respect to more traditional techniques such as Finite Elements or Differences. However, an effective reduction of the computational effort requires the solution of a number of difficulties inherent to the methods.
In this work two aspects of the method are addressed. The first one is the singular integral originated in the fundamental solution, which gives rise to diagonal terms in the final system of equations. An efficient technique for numerical integration on element boundaries is defined, upon transformation by use of the divergence theorem.
Also, a simple criterion for accurate integration of nondiagonal terms is defined, which proves computationally efficient an Sufficiently accurate.