A boundary element method for potential fields with corner singularities

Abstract

It is known that the spatial derivatives of a potential function become infinite at corner points on a boundary under certain conditions. Numerical methods such as finite and boundary element methods cannot adequately analyse the potential fields with those field singularities since they conventionally employ piecewise polynomials. This paper presents a boundary element formulation for the accurate analysis of two-dimensional potential fields with the field singularities. In this method boundary integral equations are formulated for unknown regularised functions, which are introduced by subtracting off the field singularities from the original potential function. Moreover, at the singular corner points boundary integral equations are formulated to determine the unknown expansion coefficients that characterize the behavior of the potential function around the singular corner points. By simultaneously solving the boundary integral equations for the regularized function and the expansion coefficients the original potential function is accurately determined.