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Mathematical Problems in Engineering
Volume 2015, Article ID 450980, 12 pages
Research Article

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

Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, Kimmeria, 67100 Xanthi, Greece

Received 27 November 2014; Revised 15 March 2015; Accepted 18 March 2015

Academic Editor: Yuming Qin

Copyright © 2015 P. E. Kyziropoulos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.