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Meshfree Methods for Partial Differential Equations VI pp 25–43Cite as

On the Rate of Convergence of the Hamiltonian Particle-Mesh Method

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 89))

Abstract

The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numerical 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.

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Acknowledgements

V.M. was supported in part through German Science Foundation grant LI-1530/6-1. M.O. acknowledges support through German Science Foundation grant OL-155/5-1 and through the European Science Foundation network Harmonic and Complex Analysis and Applications (HCAA). B.P. was supported by the Netherlands Organisation for Scientific Research (NWO) under the grant “Hamiltonian-based numerical methods in forced-dissipative climate prediction”.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Twente, Enschede, The Netherlands

    Bob Peeters & Onno Bokhove

  2. School of Engineering and Science, Jacobs University, 28759, Bremen, Germany

    Marcel Oliver & Vladimir Molchanov

Authors
  1. Bob Peeters
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  2. Marcel Oliver
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  3. Onno Bokhove
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  4. Vladimir Molchanov
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Correspondence to Marcel Oliver .

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Editors and Affiliations

  1. , Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, City, 53115, Germany

    Michael Griebel

  2. Institut für Parallele, und Verteilte Systeme, Universität Stuttgart, Universitätsstraße 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Peeters, B., Oliver, M., Bokhove, O., Molchanov, V. (2013). On the Rate of Convergence of the Hamiltonian Particle-Mesh Method. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_2

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