Open Access
Volume 56, Number 5, September-October 2022
Page(s) 1809 - 1841
Published online 08 August 2022
  1. A.Y. Aydemir, A unified Monte Carlo interpretation of particle simulations and applications to non-neutral plasmas. Phys. Plasmas 1 (1994) 822–831. [CrossRef] [Google Scholar]
  2. J. Benk and D. Pflüger, 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. [Google Scholar]
  3. C.K. Birdsall and D. Fuss, Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation. J. Comput. Phys. 3 (1969) 494–511. [NASA ADS] [CrossRef] [Google Scholar]
  4. C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation. CRC Press (2018). [CrossRef] [Google Scholar]
  5. H.-J. Bungartz and S. Dirnstorfer, Higher order quadrature on sparse grids. In: Computational Science – ICCS 2004, edited by M. Bubak, G.D. van Albada, P.M.A. Sloot and J. Dongarra. Lecture Notes in Computer Science. Springer, Berlin, Heidelberg (2004) 394–401. [CrossRef] [Google Scholar]
  6. H.-J. Bungartz and M. Griebel, Sparse grids. Acta Numer. 13 (2004) 147–269. [CrossRef] [MathSciNet] [Google Scholar]
  7. H.-J. Bungartz, M. Griebel, D. Röschke and C. Zenger, Pointwise convergence of the combination technique for Laplace’s equation. East-West J. Numer. Math. 2 (1994) 21–45. [Google Scholar]
  8. A. Cerfon and L. Ricketson, Sparse grid Particle-In-Cell scheme for noise reduction in beam simulations. In: 13th International Computational Accelerator Physics Conference (2019). [Google Scholar]
  9. J.M. Dawson, Particle simulation of plasmas. Rev. Mod. Phys. 55 (1983) 403–447. [CrossRef] [Google Scholar]
  10. P. Degond, F. Deluzet and D. Doyen, Asymptotic-preserving Particle-In-Cell methods for the Vlasov-Maxwell system near quasi-neutrality. Preprint arXiv:1509.04235 [physics] (2015). [Google Scholar]
  11. R.E. Denton and M. Kotschenreuther, δf Algorithm. Technical Report DOE/ET/53088-629; IFSR-629, Texas Univ., Austin, TX (United States). Inst. Fusion Studies (1993). [Google Scholar]
  12. G. Fubiani, L. Garrigues, J.P. Boeuf and J. Qiang, 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. [Google Scholar]
  13. J. Garcke, Sparse grids in a nutshell. In: Sparse Grids and Applications, edited by J. Garcke and M. Griebel. Lecture Notes in Computational Science and Engineering. Vol. 88. Springer, Berlin Heidelberg, Berlin, Heidelberg (2012) 57–80. [CrossRef] [Google Scholar]
  14. L. Garrigues, G. Fubiani and J.-P. Boeuf, Negative ion extraction via particle simulation for fusion: critical assessment of recent contributions. Nucl. Fusion 57 (2017) 014003. [CrossRef] [Google Scholar]
  15. L. Garrigues, B. Tezenas du Montcel, G. Fubiani, F. Bertomeu, F. Deluzet and J. Narski, 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. [CrossRef] [Google Scholar]
  16. L. Garrigues, B. Tezenas du Montcel, G. Fubiani and B.C.G. Reman, 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. [CrossRef] [Google Scholar]
  17. S. Gassama, É. Sonnendrücker, K. Schneider, M. Farge and M. Domingues, Wavelet denoising for postprocessing of a 2D Particle-In-Cell code. ESAIM: Proc. 16 (2007) 195–210. [CrossRef] [EDP Sciences] [Google Scholar]
  18. T. Gerstner and M. Griebel, Numerical integration using sparse grids. Numer. Algorithms 18 (1998) 209. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Griebel, Parallel multigrid methods on sparse grids. In: Multigrid Methods III, edited by W. Hackbusch and U. Trottenberg. Birkhäuser Basel, Basel (1991) 211–221. [CrossRef] [Google Scholar]
  20. M. Griebel, The combination technique for the sparse grid solution of PDE’s on multiprocessor machines. Parallel Process. Lett. 2 (1992) 61–70. [CrossRef] [Google Scholar]
  21. M. Griebel, Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing 61 (1998) 151–179. [CrossRef] [MathSciNet] [Google Scholar]
  22. E. Hockney, Computer simulation using particles. SIAM Rev. 25 (1983) 425–426. [CrossRef] [Google Scholar]
  23. N.A. Krall and A.W. Trivelpiece, Principles of plasma physics. Am. J. Phys. 41 (1973) 1380–1381. [CrossRef] [Google Scholar]
  24. S. Muralikrishnan, A.J. Cerfon, M. Frey, L.F. Ricketson and A. Adelmann, Sparse grid-based adaptive noise reduction strategy for Particle-In-Cell schemes. J. Comput. Phys. X 11 (2021) 100094. [Google Scholar]
  25. J. Petri, Non-linear evolution of the diocotron instability in a pulsar electrosphere: 2D PIC simulations. Astron. Astrophys. 503 (2009) 1–12. [Google Scholar]
  26. C. Pflaum, Convergence of the combination technique for second-order elliptic differential equations. SIAM J. Numer. Anal. 34 (1997) 2431–2455. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Philippov and A. Spitkovsky, Ab-initio pulsar magnetosphere: three-dimensional Particle-In-Cell simulations of axisymmetric pulsars. Astrophys. J. 785 (2014) L33. [CrossRef] [Google Scholar]
  28. C. Reisinger, Analysis of linear difference schemes in the sparse grid combination technique. IMA J. Numer. Anal. 33 (2013) 544–581. [CrossRef] [MathSciNet] [Google Scholar]
  29. L.F. Ricketson and A.J. Cerfon, Sparse grid techniques for Particle-In-Cell schemes. Plasma Phys. Control. Fusion 59 (2017) 024002. [CrossRef] [Google Scholar]
  30. E. Sonnendrücker, Monte Carlo methods with applications to plasma physics. In: Vorlesung (SS 2014) (2014). [Google Scholar]
  31. R.D. Sydora, Low-noise electromagnetic and relativistic Particle-In-Cell plasma simulation models. J. Comput. Appl. Math. 109 (1999) 243–259. [CrossRef] [Google Scholar]
  32. P. Tranquilli, L. Ricketson and L. Chacón, 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. [CrossRef] [Google Scholar]
  33. J.-L. Vay, C.G.R. Geddes, E. Cormier-Michel and D.P. Grote, Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame. J. Comput. Phys. 230 (2011) 5908–5929. [CrossRef] [Google Scholar]

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