Algorithm 788: Automatic Boundary Integral Equation Programs for the Planar Laplace Equation

Abstract

Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each boundary value problem as a boundary integral equation of the second kind. The Nyström method is used to solve the integral equations, and convergence of arbitrary high order is observed when the boundary data are analytic. The Kelvin transformation is introduced to allow a simple conversion between internal and external problems. Two Fortran program implementations, DRCHLT and NEUMAN, are defined, analyzed, and illustrated.