Corner singularities for elliptic problems: special basis functions versus'brute force'

A method is presented for the fast and accurate solution of elliptic bounda ry value problems on domains with corners. The method is based on integral equations and Nystrom discretization. Close to corners two representations for the solution coexist-a pointwise representation and a representation in terms of special basis functions. Mappings and kernel evaluations are cons tructed on a symmetric corner panel. In a numerical example the electrostat ic equation is solved for an array of square prisms. A dramatic improvement in efficiency over previous schemes is observed. Copyright (C) 2000 John W iley & Sons, Ltd.