Parallel \(N\)-body simulation based on the PM and P3M methods using multigrid schemes in conjunction with generic approximate sparse inverses
type: Item
instance of: scholarly article
title: Parallel \(N\)-body simulation based on the PM and P3M methods using multigrid schemes in conjunction with generic approximate sparse inverses
zbMATH Open document ID: 1394.70033
DOI: 10.1155/2015/450980
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 65N80
zbMATH DE Number: 6926375
Wikidata QID: Q59118607
author: Panagiotis E. Kyziropoulos
author: Christos K. Filelis-Papadopoulos
author: George A. Gravvanis
describes a project that uses: GenASPI
describes a project that uses: NBODY4
describes a project that uses: ParaSails
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/450980
OpenAlex ID: W2028728503
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description: scientific article; zbMATH DE number 6926375