Ten lectures on wavelets
The numerical integration of the Vlasov equation possessing an invariant
Journal of Computational Physics
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Plasma Physics Via Computer
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Journal of Computational Physics
A non-periodic 2D semi-Lagrangian Vlasov code for laser-plasma interaction on parallel computer
Journal of Computational Physics
Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space
Journal of Computational Physics
A Parallel Vlasov Solver Using a Wavelet Based Adaptive Mesh Refinement
ICPPW '05 Proceedings of the 2005 International Conference on Parallel Processing Workshops
A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation
Journal of Computational Physics
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
VALIS: A split-conservative scheme for the relativistic 2D Vlasov-Maxwell system
Journal of Computational Physics
A conservative scheme for the relativistic Vlasov-Maxwell system
Journal of Computational Physics
Hi-index | 31.46 |
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.