fmmgen: Automatic Code Generation of Operators for Cartesian Fast Multipole and Barnes-Hut Methods

The Barnes-Hut and Fast Multipole Methods are widely utilised methods applied in order to reduce the computational cost of evaluating long range forces in \(N\)-body simulations. Despite this, applying existing libraries to simple problems with higher order source points, such as dipoles, is not str...

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Bibliographic Details
Published inarXiv.org
Main Authors Pepper, Ryan Alexander, Fangohr, Hans
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.05.2020
Subjects
Cartesian coordinates
Computer algebra
Computer simulation
Dipoles
Libraries
Mathematical analysis
Multipoles
Operators (mathematics)
Physics - Computational Physics
Physics - Mesoscale and Nanoscale Physics
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Summary:The Barnes-Hut and Fast Multipole Methods are widely utilised methods applied in order to reduce the computational cost of evaluating long range forces in \(N\)-body simulations. Despite this, applying existing libraries to simple problems with higher order source points, such as dipoles, is not straightforward or efficient because individual libraries are optimised towards specific problems, normally solving for the potential and field of a set of Coulombic particles. In this paper we detail the implementation and testing of a software package, fmmgen, in which the source code for Barnes-Hut and Fast Multipole operator functions for calculating calculate the potential, field or both from arbitrary ordered sources is easily generated through symbolic algebra.
ISSN:2331-8422
DOI:10.48550/arxiv.2005.12351