Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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. 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.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an