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TECHNIQUES FOR PARALLEL, DISTRIBUTED AND CLOUD COMPUTING IN ENGINEERING
Edited by: P. Iványi and B.H.V. Topping
Parallel N-body Particle Mesh Type Methods Based on Domain Decomposition and the Multigrid Method
G.A. Gravvanis1, P.E. Kyziropoulos1, C.K. Filelis-Papadopoulos1 and C. Efthymiopoulos2
1Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, Xanthi, Greece
G.A. Gravvanis, P.E. Kyziropoulos, C.K. Filelis-Papadopoulos, C. Efthymiopoulos, "Parallel N-body Particle Mesh Type Methods Based on Domain Decomposition and the Multigrid Method", in P. Iványi and B.H.V. Topping, (Editor), "Techniques for Parallel, Distributed and Cloud Computing in Engineering", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 133-162, 2015. doi:10.4203/csets.36.7
Keywords: domain decomposition, particle mesh method, algebraic multigrid method, parallel generic approximate inverses, parallel computations.
Over the last decades, the increasing use of parallel computing has led to extensive research in the field of domain decomposition methods for solving linear or nonlinear systems of equations derived from the discretization of partial differential equations (PDEs).
Moreover, multigrid methods have been used broadly, as solvers or preconditioners for large sparse linear systems, derived from the discretization of PDEs in two and three space variables, subjected to various boundary conditions, arising from their efficiency and convergence behaviour.
N-body simulations are used extensively in physics and astronomy for the movement prediction of a dynamical system of bodies subjected to the gravitational force. Mesh type methods have been used for N-body simulations arising from the fact that they avoid the computation of all the force pairs between bodies, and instead, convert the body system into a density mesh, thus, reducing the computational cost.
Herewith, a new hybrid parallel algorithm is proposed for N-body simulations based on Mesh type methods using domain decomposition techniques in conjunction with the algebraic multigrid V-cycle method, based on modified generic factored approximate sparse inverses. The system of bodies is simulated in parallel using MPI and OpenMP environments. Moreover, a hybrid parallel algorithm is provided for the solution of the sparse linear system using non-overlapping domain decomposition in conjunction with multigrid methods. Furthermore, parallel results and theoretical estimates are provided indicating the efficiency of the proposed simulation schemes.
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