A different aproach to the singularity problem of boundary integral equations

The numerical solution of boundary integral equations imply the integration of the kernel over the boundary which is singular in free space Greenpsilas function and its spatial derivatives when the point of interest coincides with the point of integration. In this paper we present a simple and efficient method for the singularity of the kernel. We introduce the weak form of Greenpsilas function by taking the spherical mean over the singular part of Greenpsilas function. Then we introduce its nonsingular gradient and gradient divergence operators. The convergences of the numerical solutions of integral equations are shown for simple objects.