Efficient Evaluation of Ellipsoidal Harmonics for Potential Modeling
Numerical Analysis
2017-09-05 v2
Abstract
Ellipsoidal harmonics are a useful generalization of spherical harmonics but present additional numerical challenges. One such challenge is in computing ellipsoidal normalization constants which require approximating a singular integral. In this paper, we present results for approximating normalization constants using a well-known decomposition and applying tanh-sinh quadrature to the resulting integrals. Tanh-sinh has been shown to be an effective quadrature scheme for a certain subset of singular integrands. To support our numerical results, we prove that the decomposed integrands lie in the space of functions where tanh-sinh is optimal and compare our results to a variety of similar change-of-variable quadratures.
Keywords
Cite
@article{arxiv.1708.06028,
title = {Efficient Evaluation of Ellipsoidal Harmonics for Potential Modeling},
author = {Thomas S. Klotz and Jaydeep P. Bardhan and Matthew G. Knepley},
journal= {arXiv preprint arXiv:1708.06028},
year = {2017}
}