skip to main content


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

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