REMOVAL OF HYPERSINGULARITY IN A DIRECT BEM FORMULATION

Using Green's theorem, elliptic boundary value problems 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 boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.