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O. Bokhove, V. Molchanov, M. Oliver, and B. Peeters,
On the rate of convergence of the Hamiltonian particle-mesh
method,
in: Meshfree Methods for Partial Differential Equations VI (M. Griebel
and M.A. Schweitzer, eds.),
Lecture Notes in Computational Science and Engineering Vol. 89,
Springer, Berlin, 2013, pp. 25-43.
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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