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      Taylor Numbers for the Fast Multipole Method

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            Abstract

            We present a novel linear algebra formulation of the math behind the FastMultipole Method (FMM). For this, we introduce the Taylor numbers. They are polynomials governed by differential algebra but used like integers and floating points. They help simplify the FMM math and potentially any scientific programming project.

            Content

            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            28 August 2022
            Affiliations
            [1 ] none
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PPRXR9A.v1
            5de21447-a15b-41da-a414-e8bd039a88f6

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Data structures & Algorithms,Mathematical & Computational physics,Bioinformatics & Computational biology
            Fast Multipole Method (FMM),Differential Algebra (DA),Polynomial rings,Automatic differentiation,N-body problems,Molecular Dynamics (MD)

            References

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