English

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}
}
R2 v1 2026-06-21T15:34:57.283Z