A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces (Communications in Computational Physics, 2018)
We present a simple, accurate method for computing singular or nearly singularintegrals on a smooth, closed surface, such as layer potentials for harmonic functionsevaluated at points on or near the surface. The integral is computed with a regularizedkernel and corrections are added for regularization and discretization, whichare found from analysis near the singular point. The surface integrals are computedfrom a new quadrature rule using surface points which project onto grid points in coordinateplanes. The method does not require coordinate charts on the surface or specialtreatment of the singularity other than the corrections. The accuracy is about O($h^3$),where $h$ is the spacing in the background grid, uniformly with respect to the point ofevaluation, on or near the surface. Improved accuracy is obtained for points on thesurface. The treecode of Duan and Krasny for Ewald summation is used to performsums. Numerical examples are presented with a variety of surfaces.