Formulación del Método de las Soluciones Fundamentales a partir de la Integral Funcional

Abstract

In the spirit of the BEM the Method of Fundamental Solutions (MFS) is a relatively new method for the solution of certain elliptic boundary value problems. It can be viewed either as an indirect boundary element method or a modified Trefftz method in which the solution of the problem is approximated by a linear combination of fundamental solutions with sources located outside the problem domain. The locations of the sources are either preassigned or determined along with the coefficients of the linear combination so that the approximate solution satisfies the problem boundary conditions as accurately as possible. The method is relatively easy to implement, and has found extensive application in computing solutions to a broad range of applications such us in potential problems, acoustics, elastostatics and biharmonic problems.
In this work an alternative formulation of the MFS is presented which offers some advantages over the existing ones. It consists of feeding the approximation in terms of
fundamental solutions into a functional integral formulation of the problem. In doing so, the final equations contain a physical regularization parameter e. It is shown that the standard collocation method approach of the MSF is recovered from the present one in the limit e-O. Numerical examples are presented for a number of test problems and their relative merits discussed.