Higher-Order Particle Representation for Particle-in-Cell Simulations

Dominic Brown, Matthew T. Bettencourt, Steven A. Wright, Satheesh Maheswaran, John P. Jones, Stephen Jarvis

Research output: Contribution to journalArticlepeer-review


In this paper we present an alternative approach to the representation of simulation particles for unstructured electro- static and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r0. A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r0. As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories’ unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. Good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.
Original languageEnglish
Number of pages22
JournalJournal of Computational Physics
Early online date8 Mar 2021
Publication statusE-pub ahead of print - 8 Mar 2021

Bibliographical note

© 2021 Published by Elsevier Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.


  • Particle-in-Cell
  • High-order
  • Unstructured
  • Particle Representation
  • Shape Function

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