DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation

Abstract

We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.

Authors:
 [1];  [2];  [1];  [2]
  1. Stony Brook Univ., Stony Brook, NY (United States)
  2. Stony Brook Univ., Stony Brook, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE
OSTI Identifier:
1324260
Alternate Identifier(s):
OSTI ID: 1348015
Report Number(s):
BNL-112402-2016-JA
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
SC00112704; AC02-98CH10886; SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; particle method; generalized finite diference; PIC; AMR-PIC 2000 MSC: 65M06; 70F99; 76T10

Citation Formats

Wang, Xingyu, Samulyak, Roman, Jiao, Xiangmin, and Yu, Kwangmin. AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation. United States: N. p., 2016. Web. doi:10.1016/j.jcp.2016.04.037.
Wang, Xingyu, Samulyak, Roman, Jiao, Xiangmin, & Yu, Kwangmin. AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation. United States. https://doi.org/10.1016/j.jcp.2016.04.037
Wang, Xingyu, Samulyak, Roman, Jiao, Xiangmin, and Yu, Kwangmin. Tue . "AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation". United States. https://doi.org/10.1016/j.jcp.2016.04.037. https://www.osti.gov/servlets/purl/1324260.
@article{osti_1324260,
title = {AP-Cloud: Adaptive particle-in-cloud method for optimal solutions to Vlasov–Poisson equation},
author = {Wang, Xingyu and Samulyak, Roman and Jiao, Xiangmin and Yu, Kwangmin},
abstractNote = {We propose a new adaptive Particle-in-Cloud (AP-Cloud) method for obtaining optimal numerical solutions to the Vlasov–Poisson equation. Unlike the traditional particle-in-cell (PIC) method, which is commonly used for solving this problem, the AP-Cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non-uniform. Unlike other adaptive techniques for PIC, our method balances the errors in PDE discretization and Monte Carlo integration, and discretizes the differential operators using a generalized finite difference (GFD) method based on a weighted least square formulation. As a result, AP-Cloud is independent of the geometric shapes of computational domains and is free of artificial parameters. Efficient and robust implementation is achieved through an octree data structure with 2:1 balance. We analyze the accuracy and convergence order of AP-Cloud theoretically, and verify the method using an electrostatic problem of a particle beam with halo. Here, simulation results show that the AP-Cloud method is substantially more accurate and faster than the traditional PIC, and it is free of artificial forces that are typical for some adaptive PIC techniques.},
doi = {10.1016/j.jcp.2016.04.037},
journal = {Journal of Computational Physics},
number = C,
volume = 316,
place = {United States},
year = {Tue Apr 19 00:00:00 EDT 2016},
month = {Tue Apr 19 00:00:00 EDT 2016}
}

Journal Article:

Citation Metrics:
Cited by: 13 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
journal, November 1998

  • Johansen, Hans; Colella, Phillip
  • Journal of Computational Physics, Vol. 147, Issue 1
  • DOI: 10.1006/jcph.1998.5965

An embedded boundary method for elliptic and parabolic problems with interfaces and application to multi-material systems with phase transitions
journal, March 2010


Mesh refinement for particle-in-cell plasma simulations: Applications to and benefits for heavy ion fusion
journal, October 2002


Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams
journal, May 2004

  • Vay, J. -L.; Colella, P.; Kwan, J. W.
  • Physics of Plasmas, Vol. 11, Issue 5
  • DOI: 10.1063/1.1689669

Controlling self-force errors at refinement boundaries for AMR-PIC
journal, February 2010


A Finite Point Method in Computational Mechanics. Applications to Convective Transport and Fluid flow
journal, November 1996


Influence of several factors in the generalized finite difference method
journal, December 2001


An h-adaptive method in the generalized finite differences
journal, January 2003

  • Benito, J. J.; Ureña, F.; Gavete, L.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 5-6
  • DOI: 10.1016/S0045-7825(02)00594-7

The finite difference method at arbitrary irregular grids and its application in applied mechanics
journal, February 1980


Supraconvergence of a finite difference scheme for solutions in Hs(0, L)
journal, October 2005

  • Barbeiro, S.; Ferreira, J. A.; Grigorieff, R. D.
  • IMA Journal of Numerical Analysis, Vol. 25, Issue 4
  • DOI: 10.1093/imanum/dri018

Data-Parallel Octrees for Surface Reconstruction
journal, May 2011

  • Zhou, Kun; Gong, Minmin; Huang, Xin
  • IEEE Transactions on Visualization and Computer Graphics, Vol. 17, Issue 5, p. 669-681
  • DOI: 10.1109/TVCG.2010.75

Particle Methods for the One-Dimensional Vlasov–Poisson Equations
journal, February 1984

  • Cottet, G. -H.; Raviart, P. -A.
  • SIAM Journal on Numerical Analysis, Vol. 21, Issue 1
  • DOI: 10.1137/0721003

A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas
journal, January 2011

  • Wang, B.; Miller, G. H.; Colella, P.
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 6
  • DOI: 10.1137/100811805

Works referencing / citing this record:

Simulation study of the influence of experimental variations on the structure and quality of plasma liners
journal, March 2019

  • Shih, Wen; Samulyak, Roman; Hsu, Scott C.
  • Physics of Plasmas, Vol. 26, Issue 3
  • DOI: 10.1063/1.5067395

Simulations of coherent electron cooling with two types of amplifiers
journal, December 2019

  • Ma, Jun; Wang, Gang; Litvinenko, Vladimir
  • International Journal of Modern Physics A, Vol. 34, Issue 36
  • DOI: 10.1142/s0217751x19420296

Simulation study of CO 2 laser-plasma interactions and self-modulated wakefield acceleration
journal, August 2019

  • Kumar, Prabhat; Yu, Kwangmin; Zgadzaj, Rafal
  • Physics of Plasmas, Vol. 26, Issue 8
  • DOI: 10.1063/1.5095780

Adaptive Path Planning of Fiber Placement Based on Improved Method of Mesh Dynamic Representation
journal, January 2019