Analyse numérique
Fast implicit schemes for the Fokker–Planck–Landau equation
Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 809-814.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.010
Lemou, Mohammed 1; Mieussens, Luc 1

1 MIP (UMR CNRS 5640), UFR MIG, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France
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Lemou, Mohammed; Mieussens, Luc. 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. http://www.numdam.org/articles/10.1016/j.crma.2004.03.010/

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