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@ARTICLE{Shen:1030741,
      author       = {Shen, Changxiao Nigel and Cerfon, Antoine and
                      Muralikrishnan, Sriramkrishnan},
      title        = {{A} particle-in-{F}ourier method with semi-discrete energy
                      conservation for non-periodic boundary conditions},
      journal      = {Journal of computational physics},
      volume       = {519},
      issn         = {0021-9991},
      address      = {Amsterdam},
      publisher    = {Elsevier},
      reportid     = {FZJ-2024-05448},
      pages        = {113390},
      year         = {2024},
      abstract     = {We introduce a novel particle-in-Fourier (PIF) scheme based
                      on [1], [2] that extends its applicability to non-periodic
                      boundary conditions. Our method handles free space boundary
                      conditions by replacing the Fourier Laplacian operator in
                      PIF with a mollified Green's function as first introduced by
                      Vico-Greengard-Ferrando [3]. This modification yields highly
                      accurate free space solutions to the Vlasov-Poisson system,
                      while still maintaining energy conservation up to an error
                      bounded by the time step size. We also explain how to extend
                      our scheme to arbitrary Dirichlet boundary conditions via
                      standard potential theory, which we illustrate in detail for
                      Dirichlet boundary conditions on a circular boundary. We
                      support our approach with proof-of-concept numerical results
                      from two-dimensional plasma test cases to demonstrate the
                      accuracy, efficiency, and conservation properties of the
                      scheme. By avoiding grid heating and finite grid instability
                      we are able to show an order of magnitude speedup compared
                      to the standard PIC scheme for a long time integration
                      cyclotron simulation.},
      cin          = {JSC},
      ddc          = {000},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001313015300001},
      doi          = {10.1016/j.jcp.2024.113390},
      url          = {https://juser.fz-juelich.de/record/1030741},
}