Volume 28, Issue 3
Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh

Michel Mehrenberger, Laurent NavoretNhung Pham

Commun. Comput. Phys., 28 (2020), pp. 877-901.

Published online: 2020-07

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  • Abstract

In this paper, we focus on one difficulty arising in the numerical simulation of the Vlasov-Poisson system: when using a regular grid-based solver with periodic boundary conditions, perturbations present at the initial time artificially reappear at a later time. For regular finite-element mesh in velocity, we show that this recurrence time is actually linked to the spectral accuracy of the velocity quadrature when computing the charge density. In particular, choosing trigonometric quadrature weights optimally defers the occurrence of the recurrence phenomenon. Numerical results using the Semi-Lagrangian Discontinuous Galerkin and the Finite Element/Semi-Lagrangian method confirm the analysis.

  • Keywords

Finite element mesh, Vlasov-Poisson system, Semi-Lagrangian Discontinuous Galerkin method, trigonometric quadrature.

  • AMS Subject Headings

65M22, 65T40, 82D10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-877, author = {Mehrenberger , Michel and Navoret , Laurent and Pham , Nhung}, title = {Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {3}, pages = {877--901}, abstract = {

In this paper, we focus on one difficulty arising in the numerical simulation of the Vlasov-Poisson system: when using a regular grid-based solver with periodic boundary conditions, perturbations present at the initial time artificially reappear at a later time. For regular finite-element mesh in velocity, we show that this recurrence time is actually linked to the spectral accuracy of the velocity quadrature when computing the charge density. In particular, choosing trigonometric quadrature weights optimally defers the occurrence of the recurrence phenomenon. Numerical results using the Semi-Lagrangian Discontinuous Galerkin and the Finite Element/Semi-Lagrangian method confirm the analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0022}, url = {http://global-sci.org/intro/article_detail/cicp/17660.html} }
TY - JOUR T1 - Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh AU - Mehrenberger , Michel AU - Navoret , Laurent AU - Pham , Nhung JO - Communications in Computational Physics VL - 3 SP - 877 EP - 901 PY - 2020 DA - 2020/07 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0022 UR - https://global-sci.org/intro/article_detail/cicp/17660.html KW - Finite element mesh, Vlasov-Poisson system, Semi-Lagrangian Discontinuous Galerkin method, trigonometric quadrature. AB -

In this paper, we focus on one difficulty arising in the numerical simulation of the Vlasov-Poisson system: when using a regular grid-based solver with periodic boundary conditions, perturbations present at the initial time artificially reappear at a later time. For regular finite-element mesh in velocity, we show that this recurrence time is actually linked to the spectral accuracy of the velocity quadrature when computing the charge density. In particular, choosing trigonometric quadrature weights optimally defers the occurrence of the recurrence phenomenon. Numerical results using the Semi-Lagrangian Discontinuous Galerkin and the Finite Element/Semi-Lagrangian method confirm the analysis.

Michel Mehrenberger, Laurent Navoret & Nhung Pham. (2020). Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh. Communications in Computational Physics. 28 (3). 877-901. doi:10.4208/cicp.OA-2019-0022
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