An Accurate Singular Boundary Element for Two-Dimensional Problems in Potential Theory with Corner Singularities

Abstract It is well known that the spatial derivative of the potential field governed by the Laplace and Poisson equations may become infinite at re-entrant corners (in two and three dimensions) and edges (in three dimensions). In this paper, a singular element for two-dimensional boundary element analysis of corner singularities in potential problems is presented. The shape functions for the singular element are formulated based on the truncated asymptotic solution of the Laplace equation in the vicinity of a corner. Two examples are used to demonstrate the accuracy of the singular element formulation. These are the co-axial conductor problem and the parallel conductor problem. The numerical results show that this present approach gives very accurate results. The effect of the size of the singular element is also investigated.