A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system

Journal Article · Sun Aug 10 00:00:00 EDT 2008 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2008.04.031· OSTI ID:21159409

Besse, Nicolas ^[1]; Latu, Guillaume ^[2]; Ghizzo, Alain ^[1]; Sonnendruecker, Eric ^[3]; Bertrand, Pierre ^[1]

---

1. Laboratoire de Physique des Milieux Ionises et Applications, UMR CNRS 7040, Faculte de Sciences et Techniques, Universite Henri Poincare, Bd des Aiguillettes, B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex (France)
2. Laboratoire des Sciences de l'Image, de l'Informatique et de la teledetection, UMR CNRS 7005, Universite Louis Pasteur, Bd Sebastien Brant, 67400 Illkirch (France)
3. Institut de Recherche Mathematiques Avancees, UMR CNRS 7501, Universite Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg (France)

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to increase the local character in phase-space of the numerical scheme, by considering multiscale reconstruction with more compact support and by replacing the semi-Lagrangian method with more local - in space - numerical scheme as compact finite difference schemes, discontinuous-Galerkin method or finite element residual schemes which are well suited for parallel domain decomposition techniques.

• OSTI ID: 21159409
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 16 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCELERATION
APPROXIMATIONS
DISTRIBUTION FUNCTIONS
EFFICIENCY
ELECTROMAGNETIC RADIATION
ELECTRONS
ERRORS
FINITE ELEMENT METHOD
LAGRANGIAN FUNCTION
LASERS
ONE-DIMENSIONAL CALCULATIONS
PHASE SPACE
PLASMA
RELATIVISTIC RANGE
SIMULATION
TWO-DIMENSIONAL CALCULATIONS