Improved Extrapolation Technique in the Boundary Element Method to Find the Capacitances of the Unit Square and Cube

Abstract

Extrapolation of the numberNof subdivisions to infinity in the boundary element method involves fitting computed results to a polynomial in 1/N. A technique of choosing the sizes of the subdivisions in such a way that the terms of lowest order in 1/Nare eliminated, giving a more accurate extrapolation, is described. The technique is used to establish the capacitances of the unit square and cube with relative errors of 3 × 10−7and 3 × 10−6respectively.