Direct numerical evaluation of near strongly-singular integrals

In this work we present a simple and efficient numerical procedure to evaluate near strongly-singular integrals involving potential gradients for observation points at finite arbitrary small distance from the source domain. The proposed approach is based on a singularity cancellation scheme, subdividing the source domain into a disc plus truncated sub-triangles. After proper variable transformations, the kernel singularity is exactly cancelled, and the resulting integral is evaluated through a low order Gauss-Legendre quadrature scheme.