A Simple Device to Improve the Accuracy of Evaluating Weakly Singular Boundary Element Integrals

Abstract

The question of the accurate numerical evaluation of weakly singular integrals arising in the boundary element method has attracted considerable recent attention. A popular method is to use a non-linear transformation with zero derivative at the singular point to adjust the position of the Gauss-Legendre quadrature points, resulting in a more accurate evaluation of the integral. This paper presents a simple algebraic device to overcome a numerical round-off problem which has limited previous implementations of non-linear transformations. Utilization of this device allows higher orders of transformation to be used, resulting in lower relative errors in the numerical evaluation of the weakly singular integrals.