| Issue |
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 1809 - 1841 | |
| DOI | https://doi.org/10.1051/m2an/2022055 | |
| Published online | 08 August 2022 | |
Sparse grid reconstructions for Particle-In-Cell methods
1
Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France
2
CNRS, Institut de Mathématiques de Toulouse UMR 5219, F-31062 Toulouse, France
3
LAPLACE, Université de Toulouse, CNRS, INPT, UPS, 118 Route de Narbonne, F-31062 Toulouse, France
* Corresponding author: clement.guillet@math.univ-toulouse.fr
Received:
5
January
2022
Accepted:
23
June
2022
In this article, we propose and analyse Particle-In-Cell (PIC) methods embedding sparse grid reconstructions such as those introduced in Ricketson and Cerfon [Plasma Phys. Control. Fusion 59 (2017) 024002] and Muralikrishnan et al. [J. Comput. Phys. X 11 (2021) 100094]. The sparse grid reconstructions offer a significant improvement on the statistical error of PIC schemes as well as a reduction in the complexity of the problem providing the electric field. Main results on the convergence of the electric field interpolant and conservation properties are provided in this paper. Besides, tailored sparse grid reconstructions, in the frame of the offset combination technique, are proposed to introduce PIC methods with improved efficiency. The methods are assessed numerically and compared to existing PIC schemes thanks to classical benchmarks with remarkable prospects for three dimensional computations.
Mathematics Subject Classification: 65N06 / 65N75 / 65Z05
Key words: Plasma physics / Particle-In-Cell (PIC) / sparse grids / combination technique
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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