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

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

doi:10.1016/j.jcp.2021.110255

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

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

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Number of pages	22
Journal	Journal of Computational Physics
Volume	435
Early online date	8 Mar 2021
DOIs	https://doi.org/10.1016/j.jcp.2021.110255
Publication status	E-pub ahead of print - 8 Mar 2021

Bibliographical note

Keywords

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

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10.1016/j.jcp.2021.110255

HOParticles-JCP
© 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.
Accepted author manuscript, 1.04 MBLicence: CC BY-NC-ND

Cite this

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title = "Higher-Order Particle Representation for Particle-in-Cell Simulations",

abstract = "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{\textquoteright} 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.",

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AU - Brown, Dominic

AU - Bettencourt, Matthew T.

AU - Wright, Steven A.

AU - Maheswaran, Satheesh

AU - Jones, John P.

AU - Jarvis, Stephen

PY - 2021/3/8

Y1 - 2021/3/8

N2 - 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.

AB - 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.

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KW - Particle Representation

KW - Shape Function

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