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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022055
Keywords: Plasma physics, Particle-In-Cell (PIC), sparse grids, combination technique
@article{M2AN_2022__56_5_1809_0,
author = {Deluzet, Fabrice and Fubiani, Gwenael and Garrigues, Laurent and Guillet, Cl\'ement and Narski, Jacek},
title = {Sparse grid reconstructions for {Particle-In-Cell} methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1809--1841},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {5},
doi = {10.1051/m2an/2022055},
mrnumber = {4462893},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022055/}
}
TY - JOUR AU - Deluzet, Fabrice AU - Fubiani, Gwenael AU - Garrigues, Laurent AU - Guillet, Clément AU - Narski, Jacek TI - Sparse grid reconstructions for Particle-In-Cell methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 1809 EP - 1841 VL - 56 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022055/ DO - 10.1051/m2an/2022055 LA - en ID - M2AN_2022__56_5_1809_0 ER -
%0 Journal Article %A Deluzet, Fabrice %A Fubiani, Gwenael %A Garrigues, Laurent %A Guillet, Clément %A Narski, Jacek %T Sparse grid reconstructions for Particle-In-Cell methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 1809-1841 %V 56 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022055/ %R 10.1051/m2an/2022055 %G en %F M2AN_2022__56_5_1809_0
Deluzet, Fabrice; Fubiani, Gwenael; Garrigues, Laurent; Guillet, Clément; Narski, Jacek. Sparse grid reconstructions for Particle-In-Cell methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 5, pp. 1809-1841. doi: 10.1051/m2an/2022055
[1] , A unified Monte Carlo interpretation of particle simulations and applications to non-neutral plasmas. Phys. Plasmas 1 (1994) 822–831. | DOI
[2] and , Hybrid parallel solutions of the Black-Scholes PDE with the truncated combination technique. In: 2012 International Conference on High Performance Computing Simulation (HPCS) (2012) 678–683. | DOI
[3] and , Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation. J. Comput. Phys. 3 (1969) 494–511. | DOI
[4] and , Plasma Physics via Computer Simulation. CRC Press (2018). | DOI
[5] and , Higher order quadrature on sparse grids. In: Computational Science – ICCS 2004, edited by , , and . Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2004) 394–401. | MR | Zbl | DOI
[6] and , Sparse grids. Acta Numer. 13 (2004) 147–269. | MR | Zbl | DOI
[7] , , and , Pointwise convergence of the combination technique for Laplace’s equation. East-West J. Numer. Math. 2 (1994) 21–45. | MR | Zbl
[8] and , Sparse grid Particle-In-Cell scheme for noise reduction in beam simulations. In: 13th International Computational Accelerator Physics Conference (2019).
[9] , Particle simulation of plasmas. Rev. Mod. Phys. 55 (1983) 403–447. | DOI
[10] , and , Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality. Preprint [physics] (2015). | arXiv | MR
[11] and , δf Algorithm. Technical Report DOE/ET/53088-629; IFSR-629, Texas Univ., Austin, TX (United States). Inst. Fusion Studies (1993).
[12] , , and , Developpment of a hybrid MPI/OpenMP massivelly parallel 3D Particle-In-Cell model of a magnetized plasma source. In: 2015 IEEE International Conference on Plasma Sciences (ICOPS) (2015) 1.
[13] , Sparse grids in a nutshell. In: Sparse Grids and Applications, edited by and . Lecture Notes in Computational Science and Engineering. Vol. 88. Springer, Berlin Heidelberg, Berlin, Heidelberg (2012) 57–80. | MR | DOI
[14] , and , Negative ion extraction via particle simulation for fusion: critical assessment of recent contributions. Nucl. Fusion 57 (2017) 014003. | DOI
[15] , , , , and , Application of sparse grid combination techniques to low temperature plasmas Particle-In-Cell simulations. I. Capacitively coupled radio frequency discharges. J. Appl. Phys. 129 (2021) 153303. | DOI
[16] , , and , Application of sparse grid combination techniques to low temperature plasmas Particle-In-Cell simulations. II. Electron drift instability in a Hall thruster. J. Appl. Phys. 129 (2021) 153304. | DOI
[17] , , , and , Wavelet denoising for postprocessing of a 2D Particle-In-Cell code. ESAIM: Proc. 16 (2007) 195–210. | MR | Zbl | DOI
[18] and , Numerical integration using sparse grids. Numer. Algorithms 18 (1998) 209. | MR | Zbl | DOI
[19] , Parallel multigrid methods on sparse grids. In: Multigrid Methods III, edited by and . Birkhäuser Basel, Basel (1991) 211–221. | MR | Zbl | DOI
[20] , The combination technique for the sparse grid solution of PDE’s on multiprocessor machines. Parallel Process. Lett. 2 (1992) 61–70. | DOI
[21] , Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing 61 (1998) 151–179. | MR | Zbl | DOI
[22] , Computer simulation using particles. SIAM Rev. 25 (1983) 425–426. | DOI
[23] and , Principles of plasma physics. Am. J. Phys. 41 (1973) 1380–1381. | DOI
[24] , , , and , Sparse grid-based adaptive noise reduction strategy for Particle-In-Cell schemes. J. Comput. Phys. X 11 (2021) 100094. | MR
[25] , Non-linear evolution of the diocotron instability in a pulsar electrosphere: 2D PIC simulations. Astron. Astrophys. 503 (2009) 1–12. | Zbl | DOI
[26] , Convergence of the combination technique for second-order elliptic differential equations. SIAM J. Numer. Anal. 34 (1997) 2431–2455. | MR | Zbl | DOI
[27] and , Ab-initio pulsar magnetosphere: three-dimensional Particle-In-Cell simulations of axisymmetric pulsars. Astrophys. J. 785 (2014) L33. | DOI
[28] , Analysis of linear difference schemes in the sparse grid combination technique. IMA J. Numer. Anal. 33 (2013) 544–581. | MR | Zbl | DOI
[29] and , Sparse grid techniques for Particle-In-Cell schemes. Plasma Phys. Control. Fusion 59 (2017) 024002. | DOI
[30] , Monte Carlo methods with applications to plasma physics. In: Vorlesung (SS 2014) (2014).
[31] , Low-noise electromagnetic and relativistic Particle-In-Cell plasma simulation models. J. Comput. Appl. Math. 109 (1999) 243–259. | Zbl | DOI
[32] , and , A deterministic verification strategy for electrostatic Particle-In-Cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions. J. Comput. Phys. 448 (2022) 110751. | MR | DOI
[33] , , and , Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame. J. Comput. Phys. 230 (2011) 5908–5929. | DOI
Cité par Sources :
