The solution of poisson's equation for isolated source distributions

The potential due to an isolated finite distribution of sources satisfies a zero condition at infinity in three dimensions, or a logarithmic condition in two. It may be evaluated on a finite mesh by means of a fast potential solver for the mesh, combined with a procedure for the potential on the mesh boundary. This paper describes a way of calculating the boundary potential by finding a set of correction charges on the boundary only, and convolving them with a suitable Green's function. The advantage over the usual convolution techniques is that mesh doubling is needed for boundary points only. The process is equivalent to convolving the source distribution with the Green's function, but requires less storage and computer time. The choice of Green's function is constrained by the finite difference approximation used for the Laplace operator.