@Article{CiCP-20-3,
author = {},
title = {A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces},
journal = {Communications in Computational Physics},
year = {2016},
volume = {20},
number = {3},
pages = {733--753},
abstract = {<p style="text-align: justify;">We present a simple, accurate method for computing singular or nearly singular
integrals on a smooth, closed surface, such as layer potentials for harmonic functions
evaluated at points on or near the surface. The integral is computed with a regularized
kernel and corrections are added for regularization and discretization, which
are found from analysis near the singular point. The surface integrals are computed
from a new quadrature rule using surface points which project onto grid points in coordinate
planes. The method does not require coordinate charts on the surface or special
treatment 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 of
evaluation, on or near the surface. Improved accuracy is obtained for points on the
surface. The treecode of Duan and Krasny for Ewald summation is used to perform
sums. Numerical examples are presented with a variety of surfaces.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.030815.240216a},
url = {https://global-sci.com/article/80216/a-simple-method-for-computing-singular-or-nearly-singular-integrals-on-closed-surfaces}
}