Fast implicit schemes for the Fokker–Planck–Landau equation

Mohammed Lemou; Luc Mieussens

doi:10.1016/j.crma.2004.03.010

Analyse numérique

Fast implicit schemes for the Fokker–Planck–Landau equation

Presented by: Philippe G. Ciarlet

Mohammed Lemou ¹ ; Luc Mieussens ¹

¹ MIP (UMR CNRS 5640), UFR MIG, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France

Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 809-814.

Abstract
Résumé

We propose new implicit schemes to solve the homogeneous and isotropic Fokker–Planck–Landau equation. These schemes have conservation and entropy properties. Moreover, they allow for large time steps (of the order of the physical relaxation time), contrary to usual explicit schemes. We use in particular fast linear Krylov solvers like the GMRES method. These schemes allow an important gain in terms of CPU time, with the same accuracy as explicit schemes. This work is a first step to the development of fast implicit schemes to solve more realistic kinetic models.

Nous proposons de nouveaux schémas implicites pour résoudre l'équation de Fokker–Planck–Landau homogène isotrope. Ces schémas possèdent des propriétés de conservation et d'entropie. Ils permettent l'utilisation de pas de temps de l'ordre du temps de relaxation physique, contrairement aux schémas explicites usuels. Nous utilisons en particulier des solveurs linéaires rapides de type Krylov comme la méthode GMRES. Ces schémas offrent un gain important en temps CPU avec une précision comparable à celle des schémas explicites. Ce travail constitue une première étape en vue du développement de schémas implicites rapides pour résoudre des équations cinétiques plus réalistes.

Received: 2003-08-06
Accepted: 2004-03-09
Published online: 2004-04-09

DOI: 10.1016/j.crma.2004.03.010

Author's affiliations:

Mohammed Lemou ¹; Luc Mieussens ¹

¹ MIP (UMR CNRS 5640), UFR MIG, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France

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     author = {Mohammed Lemou and Luc Mieussens},
     title = {Fast implicit schemes for the {Fokker{\textendash}Planck{\textendash}Landau} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {809--814},
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     number = {10},
     year = {2004},
     doi = {10.1016/j.crma.2004.03.010},
     language = {en},
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Mohammed Lemou; Luc Mieussens. Fast implicit schemes for the Fokker–Planck–Landau equation. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 809-814. doi : 10.1016/j.crma.2004.03.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.010/

References
Cited by

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[7] M. Lemou, L. Mieussens, Fast implicit schemes for the homogeneous Fokker–Planck–Landau equation, in preparation

[8] Y. Saad Iterative methods for sparse linear systems, 2000 http://www-users.cs.umn.edu/~saad/books.html

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