Recurrence Phenomenon for Vlasov-Poisson Simulations on Regular Finite Element Mesh (Communications in Computational Physics, 2020)
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 thisrecurrence time is actually linked to the spectral accuracy of the velocity quadraturewhen computing the charge density. In particular, choosing trigonometric quadratureweights 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.