Multipole expansion BEM for simultaneous Poisson's equations

摘要

A boundary element method for simultaneous Poisson's equations is presented to solve large scale problems governed by Poisson's equation using multipole expansions of the fundamental solutions. Original Poisson's equation is approximated a set of Poisson's equations and an integral representation for the set of differential equations is derived. The fundamental solutions of the coupled Poisson equations consist of the fundamental solution of Laplace's equation, biharmonic function, and triharmonic function. Multipole expansions of these fundamental solutions are used in the evaluation of the boundary integral equations. The effectiveness of the present formulation is demonstrated through a numerical example.