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Title: Derivation and efficient implementation of the fast multipole method

Abstract

The fast multipole method (FMM) of Greengard evaluates Coulomb interactions of point charges with computational requirements that increase linearly with the number of particles. In this work, the central transformations of the FMM are obtained in a very compact manner from simple algebraic manipulations of two addition theorems. The intermediate multipole and Taylor expansions are defined differently from previous work to yield simplified and more efficient transformations. Error estimates are obtained due to the effect of multipole truncation and the use of the multipole to Taylor transformation operator. Efficient implementation of the FMM for potential and forces is discussed, and calculations are presented that probe the accuracy and performance of the method.

Authors:
;  [1]
  1. Department of Chemistry, University of California, Berkeley, Berkeley, California 94720 (United States)
Publication Date:
OSTI Identifier:
7032711
DOE Contract Number:  
FG05-93ER81643
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics; (United States)
Additional Journal Information:
Journal Volume: 101:8; Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; POINT CHARGE; COULOMB FIELD; MULTIPOLES; SERIES EXPANSION; TRANSFORMATIONS; ELECTRIC CHARGES; ELECTRIC FIELDS; 664100* - Theory of Electronic Structure of Atoms & Molecules- (1992-)

Citation Formats

White, C A, and Head-Gordon, M. Derivation and efficient implementation of the fast multipole method. United States: N. p., 1994. Web. doi:10.1063/1.468354.
White, C A, & Head-Gordon, M. Derivation and efficient implementation of the fast multipole method. United States. https://doi.org/10.1063/1.468354
White, C A, and Head-Gordon, M. 1994. "Derivation and efficient implementation of the fast multipole method". United States. https://doi.org/10.1063/1.468354.
@article{osti_7032711,
title = {Derivation and efficient implementation of the fast multipole method},
author = {White, C A and Head-Gordon, M},
abstractNote = {The fast multipole method (FMM) of Greengard evaluates Coulomb interactions of point charges with computational requirements that increase linearly with the number of particles. In this work, the central transformations of the FMM are obtained in a very compact manner from simple algebraic manipulations of two addition theorems. The intermediate multipole and Taylor expansions are defined differently from previous work to yield simplified and more efficient transformations. Error estimates are obtained due to the effect of multipole truncation and the use of the multipole to Taylor transformation operator. Efficient implementation of the FMM for potential and forces is discussed, and calculations are presented that probe the accuracy and performance of the method.},
doi = {10.1063/1.468354},
url = {https://www.osti.gov/biblio/7032711}, journal = {Journal of Chemical Physics; (United States)},
issn = {0021-9606},
number = ,
volume = 101:8,
place = {United States},
year = {1994},
month = {10}
}