REMOVAL OF HYPERSINGULARITY IN A DIRECT BEM FORMULATION

Abstract

Using Green’s theorem, elliptic boundary value prob-
lems can be converted to boundary integral equations. A numerical
methods for boundary integral equations are boundary elementary
method(BEM). BEM has advantages over finite element method(FEM)
whenever the fundamental solutions are known. Helmholtz type
equations arise naturally in many physical applications. In a bound-
ary integral formulation for the exterior Neumann there occurs a hy-
persingular operator which exhibits a strong singularity like 1/|x−y|^3
and hence is not an integrable function. In this paper we are going
to remove this hypersingularity by reducing the regularity of test
functions.