Noiseless VlasovPoisson simulations with linearly transformed particles
We introduce a deterministic discreteparticle simulation approach, the LinearlyTransformed ParticleInCell (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 SemiLagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying LinearlyTransformed 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 »
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); CNRS, UMR 7598, Lab. JacquesLouis Lions, Paris (France); UPMC Univ. Paris 06, UMR 7598, Lab. JacquesLouis Lions, Paris (France)
 IRMA, UMR 7501, Univ. de Strasbourg & CNRS, Strasbourg Cedex (France); Projectteam CALVI, Strasbourg Cedex (France)
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL696802
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 275; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab., Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; particle method; Vlasov–Poisson equation; plasma; noiseless method; remapping; beam halo simulations
 OSTI Identifier:
 1281673
Pinto, Martin C., Sonnendrucker, Eric, Friedman, Alex, Grote, David P., and Lund, Steve M.. Noiseless VlasovPoisson simulations with linearly transformed particles. United States: N. p.,
Web. doi:10.1016/j.jcp.2014.06.032.
Pinto, Martin C., Sonnendrucker, Eric, Friedman, Alex, Grote, David P., & Lund, Steve M.. Noiseless VlasovPoisson simulations with linearly transformed particles. United States. doi:10.1016/j.jcp.2014.06.032.
Pinto, Martin C., Sonnendrucker, Eric, Friedman, Alex, Grote, David P., and Lund, Steve M.. 2014.
"Noiseless VlasovPoisson simulations with linearly transformed particles". United States.
doi:10.1016/j.jcp.2014.06.032. https://www.osti.gov/servlets/purl/1281673.
@article{osti_1281673,
title = {Noiseless VlasovPoisson simulations with linearly transformed particles},
author = {Pinto, Martin C. and Sonnendrucker, Eric and Friedman, Alex and Grote, David P. and Lund, Steve M.},
abstractNote = {We introduce a deterministic discreteparticle simulation approach, the LinearlyTransformed ParticleInCell (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 SemiLagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying LinearlyTransformed 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 formation 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 stateoftheart, highresolution Vlasov schemes.},
doi = {10.1016/j.jcp.2014.06.032},
journal = {Journal of Computational Physics},
number = C,
volume = 275,
place = {United States},
year = {2014},
month = {6}
}