On the Rate of Convergence of the Hamiltonian Particle-Mesh Method
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.
KeywordsHamiltonian particle-mesh method Rate of convergence Numerical tests
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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