On the rate of convergence of the Hamiltonian particle-mesh method.

B.W.I. Peeters, Marcel Oliver, Onno Bokhove, Vladimir Molchanov

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    Abstract

    The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numer- ical short-time study of the rate of convergence of HPM in terms of its three main governing parameters. We find that the rate of convergence is much better than the best available theoretical estimates. Our results indicate that HPM performs best when the number of particles is on the order of the number of grid cells, the HPM global smoothing kernel has fast decay in Fourier space, and the HPM local interpolation kernel is a cubic spline.
    Original languageUndefined
    Title of host publicationMeshfree Methods for Partial Differential Equations VI
    EditorsM. Griebel, M.A. Schweitzer
    Place of PublicationBerlin
    PublisherSpringer
    Pages25-43
    Number of pages19
    ISBN (Print)978-3-642-32978-4
    DOIs
    Publication statusPublished - 2013

    Publication series

    NameLecture Notes in Computational Science and Engineering
    PublisherSpringer Verlag
    Number89
    Volume89
    ISSN (Print)1439-7358

    Keywords

    • EWI-23121
    • Rate of convergence
    • METIS-296326
    • Hamiltonian particle-mesh method
    • IR-84333
    • Numerical tests

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