[2311.09379] A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties
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Mathematics > Numerical Analysis

arXiv:2311.09379 (math)
[Submitted on 15 Nov 2023 (v1), last revised 13 May 2024 (this version, v2)]

Title:A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties

Authors:Philipp Krah, Xi-Yuan Yin, Julius Bergmann, Jean-Christophe Nave, Kai Schneider
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Abstract:We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in linear time is obtained. Global third-order convergence in space and time is shown and conservation properties are assessed. For benchmarking, we consider linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method. The extreme fine-scale resolution features are illustrated showing the method's capabilities to efficiently treat filamentation in fusion plasma simulations.
Comments: Code is available at this https URL
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph); Plasma Physics (physics.plasm-ph)
Cite as: arXiv:2311.09379 [math.NA]
  (or arXiv:2311.09379v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2311.09379
Journal reference: Commun. Comput. Phys., 35 (2024), pp. 905-937
Related DOI: https://doi.org/10.4208/cicp.OA-2024-0012

Submission history

From: Philipp Krah [view email]
[v1] Wed, 15 Nov 2023 21:13:16 UTC (8,047 KB)
[v2] Mon, 13 May 2024 15:04:49 UTC (9,690 KB)
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