The Spherical Multipole Expansion of a Triangle
Abstract
We describe a technique to analytically compute the multipole moments of a charge distribution confined to a planar triangle, which may be useful in solving the Laplace equation using the fast multipole boundary element method (FMBEM) and for charged particle tracking. This algorithm proceeds by performing the necessary integration recursively within a specific coordinate system, and then transforming the moments into the global coordinate system through the application of rotation and translation operators. This method has been implemented and found use in conjunction with a simple piecewise constant collocation scheme, but is generalizable to non-uniform charge densities. When applied to low aspect ratio () triangles and expansions with degree up to 32, it is accurate and efficient compared to simple two-dimensional Gauss-Legendre quadrature.
Cite
@article{arxiv.1403.5362,
title = {The Spherical Multipole Expansion of a Triangle},
author = {John P. Barrett and Joseph A. Formaggio and Thomas J. Corona},
journal= {arXiv preprint arXiv:1403.5362},
year = {2015}
}
Comments
20 pages, 7 figures, changed formatting and reduced verbosity of background material, consolidated derivation to shorten length and updated numerical tests and figures to better show difference between algorithms