The geometric solution of Laplace's equation (Q1913710)

This paper presents a new numerical method for the fast solution of the two-dimensional Laplace equation in exterior and interior domains with complicated boundaries. The method is based on a formula first stated in 1891 by \textit{J. J. Thomson}, the discoverer of the electron, and utilizes the concept of representing equipotential surfaces by polynomials for the fast tracing of these surfaces. The method requires \(O(M)\) computations, where \(M\) is the number of points inside the domain at which the solution is computed.