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:
-
- Stony Brook Univ., Stony Brook, NY (United States)
- 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}
}
Web of Science
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