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

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; Yu, Kwangmin

doi:10.1016/j.jcp.2016.04.037

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

Journal Article · Tue Apr 19 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2016.04.037· OSTI ID:1324260

Wang, Xingyu ^[1]; Samulyak, Roman ^[2]; Jiao, Xiangmin ^[1]; Yu, Kwangmin ^[2]

Stony Brook Univ., Stony Brook, NY (United States)
Stony Brook Univ., Stony Brook, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE

Grant/Contract Number:: SC00112704; AC02-98CH10886; SC0012704

OSTI ID:: 1324260

Alternate ID(s):: OSTI ID: 1348015

Report Number(s):: BNL-112402-2016-JA

Journal Information:: Journal of Computational Physics, Vol. 316, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 13 works

Citation information provided by
Web of Science

References (13)

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains Johansen, Hans; Colella, Phillip Journal of Computational Physics, Vol. 147, Issue 1 https://doi.org/10.1006/jcph.1998.5965	journal	November 1998
An embedded boundary method for elliptic and parabolic problems with interfaces and application to multi-material systems with phase transitions Wang, Shuqiang; Samulyak, Roman; Guo, Tongfei Acta Mathematica Scientia, Vol. 30, Issue 2 https://doi.org/10.1016/S0252-9602(10)60059-8	journal	March 2010
Mesh refinement for particle-in-cell plasma simulations: Applications to and benefits for heavy ion fusion Vay, J. -L.; Colella, P.; McCORQUODALE, P. Laser and Particle Beams, Vol. 20, Issue 4 https://doi.org/10.1017/S0263034602204139	journal	October 2002
Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams Vay, J. -L.; Colella, P.; Kwan, J. W. Physics of Plasmas, Vol. 11, Issue 5 https://doi.org/10.1063/1.1689669	journal	May 2004
Controlling self-force errors at refinement boundaries for AMR-PIC Colella, Phillip; Norgaard, Peter C. Journal of Computational Physics, Vol. 229, Issue 4 https://doi.org/10.1016/j.jcp.2009.07.004	journal	February 2010
A Finite Point Method in Computational Mechanics. Applications to Convective Transport and Fluid flow OÑAte, E.; Idelsohn, S.; Zienkiewicz, O. C. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 22 https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R	journal	November 1996
Influence of several factors in the generalized finite difference method Benito, J. J.; Ureña, F.; Gavete, L. Applied Mathematical Modelling, Vol. 25, Issue 12 https://doi.org/10.1016/S0307-904X(01)00029-4	journal	December 2001
An h-adaptive method in the generalized finite differences Benito, J. J.; Ureña, F.; Gavete, L. Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 5-6 https://doi.org/10.1016/S0045-7825(02)00594-7	journal	January 2003
The finite difference method at arbitrary irregular grids and its application in applied mechanics Liszka, T.; Orkisz, J. Computers & Structures, Vol. 11, Issue 1-2 https://doi.org/10.1016/0045-7949(80)90149-2	journal	February 1980
Supraconvergence of a finite difference scheme for solutions in Hs(0, L) Barbeiro, S.; Ferreira, J. A.; Grigorieff, R. D. IMA Journal of Numerical Analysis, Vol. 25, Issue 4 https://doi.org/10.1093/imanum/dri018	journal	October 2005
Data-Parallel Octrees for Surface Reconstruction Zhou, Kun; Gong, Minmin; Huang, Xin IEEE Transactions on Visualization and Computer Graphics, Vol. 17, Issue 5, p. 669-681 https://doi.org/10.1109/TVCG.2010.75	journal	May 2011
Particle Methods for the One-Dimensional Vlasov–Poisson Equations Cottet, G. -H.; Raviart, P. -A. SIAM Journal on Numerical Analysis, Vol. 21, Issue 1 https://doi.org/10.1137/0721003	journal	February 1984
A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas Wang, B.; Miller, G. H.; Colella, P. SIAM Journal on Scientific Computing, Vol. 33, Issue 6 https://doi.org/10.1137/100811805	journal	January 2011

Cited By (4)

Simulation study of the influence of experimental variations on the structure and quality of plasma liners Shih, Wen; Samulyak, Roman; Hsu, Scott C. Physics of Plasmas, Vol. 26, Issue 3 https://doi.org/10.1063/1.5067395	journal	March 2019
Simulations of coherent electron cooling with two types of amplifiers Ma, Jun; Wang, Gang; Litvinenko, Vladimir International Journal of Modern Physics A, Vol. 34, Issue 36 https://doi.org/10.1142/s0217751x19420296	journal	December 2019
Simulation study of CO ₂ laser-plasma interactions and self-modulated wakefield acceleration Kumar, Prabhat; Yu, Kwangmin; Zgadzaj, Rafal Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5095780	journal	August 2019
Adaptive Path Planning of Fiber Placement Based on Improved Method of Mesh Dynamic Representation Zhang, Leen; Wang, Xiaoping; Pei, Jingyu Applied Composite Materials, Vol. 26, Issue 3 https://doi.org/10.1007/s10443-018-9751-8	journal	January 2019

Similar Records

AP-Cloud: Adaptive Particle-in-Cloud method for optimal solutions to Vlasov–Poisson equation

Journal Article · Fri Jul 01 00:00:00 EDT 2016 · Journal of Computational Physics · OSTI ID:1324260

Wang, Xingyu; Samulyak, Roman; Jiao, Xiangmin; +1 more

SPACE: 3D parallel solvers for Vlasov-Maxwell and Vlasov-Poisson equations for relativistic plasmas with atomic transformations

Journal Article · Fri Apr 29 00:00:00 EDT 2022 · Computer Physics Communications · OSTI ID:1324260

Yu, Kwangmin; Kumar, Prabhat; Yuan, Shaohua; +2 more

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

Journal Article · Tue Jun 06 00:00:00 EDT 2023 · Journal of Computational Physics · OSTI ID:1324260

Pagliantini, Cecilia; Delzanno, Gian Luca; Markidis, Stefano

Related Subjects

97 MATHEMATICS AND COMPUTING
particle method
generalized finite diference
PIC
AMR-PIC 2000 MSC: 65M06
70F99
76T10

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

Citation Formats

References (13)

Cited By (4)

Similar Records

Related Subjects