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Parallel N-Body Simulation Based on the PM and P3M Methods Using Multigrid Schemes in conjunction with Generic Approximate Sparse Inverses

机译：基于PM和P3M方法的并行N体仿真，使用多网格方案与通用近似稀疏逆相结合

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摘要

During the last decades, Multigrid methods have been extensively used for solving large sparse linear systems. Considering their efficiency and the convergence behavior, Multigrid methods are used in many scientific fields as solvers or preconditioners. Herewith, we propose two hybrid parallel algorithms for N-Body simulations using the Particle Mesh method and the Particle Particle Particle Mesh method, respectively, based on the V-Cycle Multigrid method in conjunction with Generic Approximate Sparse Inverses. The N-Body problem resides in a three-dimensional torus space, and the bodies are subject only to gravitational forces. In each time step of the above methods, a large sparse linear system is solved to compute the gravity potential at each nodal point in order to interpolate the solution to each body. Then the Velocity Verlet method is used to compute the new position and velocity from the acceleration of each respective body. Moreover, a parallel Multigrid algorithm, with a truncated approach in the levels computed in parallel, is proposed for solving large linear systems. Furthermore, parallel results are provided indicating the efficiency of the proposed Multigrid N-Body scheme. Theoretical estimates for the complexity of the proposed simulation schemes are provided.
机译：在过去的几十年中，Multigrid方法已广泛用于解决大型稀疏线性系统。考虑到它们的效率和收敛行为，Multigrid方法在许多科学领域中用作求解器或预处理器。因此，我们结合V-Cycle Multigrid方法和通用近似稀疏逆，分别提出了两种混合并行算法，分别用于使用粒子网格方法和粒子颗粒粒子网格方法进行N体仿真。 N体问题存在于三维环面空间中，并且物体仅受到重力的作用。在上述方法的每个时间步中，求解一个大型的稀疏线性系统以计算每个节点上的重力势，以便将解插值到每个物体。然后使用速度Verlet方法根据各个身体的加速度来计算新的位置和速度。此外，提出了一种并行Multigrid算法，该算法在并行计算的级别中采用了截断方法，用于求解大型线性系统。此外，提供的并行结果表明了所提出的Multigrid N-Body方案的效率。提供了所提出的仿真方案的复杂性的理论估计。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第6期|450980.1-450980.12|共12页
  • 作者

    Kyziropoulos P. E.; Filelis-Papadopoulos C. K.; Gravvanis G. A.;

  • 作者单位

    Democritus Univ Thrace, Sch Engn, Dept Elect & Comp Engn, GR-67100 Xanthi, Greece.;

    Democritus Univ Thrace, Sch Engn, Dept Elect & Comp Engn, GR-67100 Xanthi, Greece.;

    Democritus Univ Thrace, Sch Engn, Dept Elect & Comp Engn, GR-67100 Xanthi, Greece.;

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