2007 / June Volume 2 No.2
Time implicit schemes and fast approximations of the Fokker-Planck-Landau equation
| Published Date |
2007 / June
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| Title | Time implicit schemes and fast approximations of the Fokker-Planck-Landau equation |
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| Pagination | 533-567 |
| Abstract | In this paper, we are concerned with numerical approximations of the Fokker-Planck-Landau equation which is a kinetic model used to describe the evolution of charged particles in a plasma. In this model, the particle interactions (or collisions) are
taken into account by a nonlocal and nonlinear diffusion operator acting on the velocity dependence of the particle distribution function. In a first part of this work, we investigate different strategies to perform efficient time implicit discretisations, while, in the second part, we review various numerical approximations
of the collision operator. Both the time discretisation and the approximations of the collision operator are shown to satisfy some
important physical properties of conservation and entropy, and to reach the right steady states. Furthermore, various accelerations techniques are used to construct such approximations which would make possible their use in a more realistic setting (inhomogeneous cases). In particular, we combine two new strategies to rapidly and efficiently solve the FPL equation: the first one concerns the time discretisation using time implicit schemes with Krylov solvers, and the second one uses the approximation of the collision operator using the wavelet approximation theory.
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| AMS Subject Classification |
82C40, 82D10, 82C80, 65M06, 65Y20, 65F10
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| Received |
2005-05-19
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