A Simple Transformation for the Numerical Evaluation of Near Strongly Singular Integrals

A simple transformation using a singularity cancellation technique is presented that enables accurate and efficient computation of near strongly singular integrals involving the gradient of Helmholtz-type potentials for projected observation points that lie external to the source element. Unlike previous Duffy-like transformations, the coordinate reference is offset from the projection of the observation point onto the plane containing the source element. In many cases, this permits highly accurate results without the splitting of the source element. When splitting is required, high-aspect-ratio subtriangles are easily avoided.