Radial Integration Scheme for Handling Weakly Singular and Near-Singular Potential Integrals

An efficient integration scheme is proposed for calculating weakly singular and near-singular potential integrals over planar triangles, with an essential improvement over the original polar integration. The reason for the problem of slow convergence of polar integration is revealed according to some careful investigations. A new technique of smoothing integrand based on variable transformation is presented to guarantee the smoothness of the integral kernel, which results in much faster convergence than that of the polar integration. Some numerical results are given to demonstrate the capability of our proposed scheme for achieving high accuracy as well as rapid convergence rate in several numerical experiments.