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

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.

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

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

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

OSTI ID:: 1324260

Alternate ID(s):: OSTI ID: 1348015
OSTI ID: 22572331

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

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

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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