On well-separated sets and fast multipole methods
Numerical Analysis
2011-08-11 v3 Data Structures and Algorithms
Numerical Analysis
Abstract
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures.
Keywords
Cite
@article{arxiv.1006.2269,
title = {On well-separated sets and fast multipole methods},
author = {Stefan Engblom},
journal= {arXiv preprint arXiv:1006.2269},
year = {2011}
}