On well-separated sets and fast multipole methods

Details On well-separated sets and fast multipole methods On well-separated sets and fast multipole methods

2010-06-11

arxiv.org/abs/1006.2269v3

Appl. Numer. Math. 61(10):1096--1102, 2011

Mathematics

Numerical Analysis

Scientific paper

10.1016/j.apnum.2011.06.011

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.

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