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Title: Noiseless Vlasov-Poisson simulations with linearly transformed particles

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formationmore » in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.« less
 [1] ;  [2] ;  [3] ;  [3] ;  [3]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); CNRS, UMR 7598, Lab. Jacques-Louis Lions, Paris (France); UPMC Univ. Paris 06, UMR 7598, Lab. Jacques-Louis Lions, Paris (France)
  2. IRMA, UMR 7501, Univ. de Strasbourg & CNRS, Strasbourg Cedex (France); Project-team CALVI, Strasbourg Cedex (France)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0021-9991
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 275; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Lawrence Livermore National Lab., Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
70 PLASMA PHYSICS AND FUSION; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE particle method; Vlasov–Poisson equation; plasma; noiseless method; remapping; beam halo simulations