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We present a simple, accurate method for computing singular or nearlysingular integrals on a smooth, closed surface, such as layer potentials forharmonic functions evaluated at points on or near the surface. The integral iscomputed with a regularized kernel and corrections are added for regularizationand discretization, which are found from analysis near the singular point. Thesurface integrals are computed from a new quadrature rule using surface pointswhich project onto grid points in coordinate planes. The method does notrequire coordinate charts on the surface or special treatment of thesingularity 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 pointof evaluation, on or near the surface. Improved accuracy is obtained for pointson the surface. The treecode of Duan and Krasny for Ewald summation is used toperform sums. Numerical examples are presented with a variety of surfaces.

A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces