Variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system

Jose A. Carrillo, Li Wang, Wuzhe Xu, Ming Yan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an implicit-explicit framework, wherein the stiff terms coming from the collision and field effects are solved implicitly while the convection terms are solved explicitly. To treat the implicit part, we propose a variational approach by viewing it as a Wasserstein gradient flow of the relative entropy, and solve it via a proximal quasi-Newton method. In so doing we get positivity and asymptotic preservation for free. The method is also massively parallelizable and thus suitable for high dimensional problems. We further show that the convergence of our implicit solver is uniform across different scales. A suite of numerical examples are presented at the end to validate the performance of the proposed scheme.

Original languageEnglish (US)
Pages (from-to)478-505
Number of pages28
JournalMultiscale Modeling and Simulation
Volume19
Issue number1
DOIs
StatePublished - Mar 16 2021

Bibliographical note

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics

Keywords

  • Asymptotic preserving
  • High field limit
  • Variational scheme

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