@article{10.1016/j.jcp.2013.03.008,
    abstract = "The understanding of particle dynamics in N-body problems is of importance to many applications in astrophysics, molecular dynamics and cloud/plasma physics where the theoretical representation results in a coupled system of equations for a large number of entities. This paper concerns algorithms for solving a specific N-body problem, namely, a system of disturbance velocities for hydrodynamically interacting particles in a particle-laden turbulent flow. The system is derived from the improved superposition method of [1]. Targeting for scalable computations on petascale computers, we have carried out a thorough study of a parallel implementation of GMRes with different features, such as preconditioners, matrix-free and parallel sparse representation of the matrix through 1D and 2D spatial domain decompositions. Gauss-Seidel method is also studied as a reference iterative algorithm. The range of conditions for efficiency and failure of each method is discussed in detail. Through perturbation analysis, we have conducted a series of experiments to understand the effect of particle sizes, interaction symmetry, inter-particle distances and interaction truncation on the eigenvalues and normality of the linear system. For situations where the system is ill-conditioned, we introduce a restricted Schwarz type preconditioner. We verified the parallel efficiency of the preconditioner using 1D domain decomposition on a parallel machine. A benchmark problem of particle laden turbulence at 5123 resolution with 2 × 106 particles is studied to understand the scalability of the proposed methods on parallel machines. We have developed a stable and highly scalable parallel solver with an affordable computational cost even for ill-conditioned systems through preconditioning. On 64 cores, using GMRes in 2D domain decomposition, we achieved a speed-up of \textasciitilde 5.6x (relative to 1D domain decomposition on the same number of processors). Our complexity analysis showed that for large N-body problems, the proposed GMRes scheme scales well for moderate to large number of processors in current tera to petascale computers. © 2013 Elsevier Inc.",
    year = "2013",
    title = "Analysis and parallel implementation of a forced N-body problem",
    volume = "245",
    pages = "235-258",
    doi = "10.1016/j.jcp.2013.03.008",
    journal = "Journal of Computational Physics"
}

{"_id":"5wyoZrgcEh4AfcPk5","bibbaseid":"anonymous-analysisandparallelimplementationofaforcednbodyproblem-2013","downloads":0,"creationDate":"2017-03-31T20:15:33.079Z","title":"Analysis and parallel implementation of a forced N-body problem","author_short":null,"year":2013,"bibtype":"article","biburl":"https://1fichier.com/?j9cpurkmnv","bibdata":{"bibtype":"article","type":"article","abstract":"The understanding of particle dynamics in N-body problems is of importance to many applications in astrophysics, molecular dynamics and cloud/plasma physics where the theoretical representation results in a coupled system of equations for a large number of entities. This paper concerns algorithms for solving a specific N-body problem, namely, a system of disturbance velocities for hydrodynamically interacting particles in a particle-laden turbulent flow. The system is derived from the improved superposition method of [1]. Targeting for scalable computations on petascale computers, we have carried out a thorough study of a parallel implementation of GMRes with different features, such as preconditioners, matrix-free and parallel sparse representation of the matrix through 1D and 2D spatial domain decompositions. Gauss-Seidel method is also studied as a reference iterative algorithm. The range of conditions for efficiency and failure of each method is discussed in detail. Through perturbation analysis, we have conducted a series of experiments to understand the effect of particle sizes, interaction symmetry, inter-particle distances and interaction truncation on the eigenvalues and normality of the linear system. For situations where the system is ill-conditioned, we introduce a restricted Schwarz type preconditioner. We verified the parallel efficiency of the preconditioner using 1D domain decomposition on a parallel machine. A benchmark problem of particle laden turbulence at 5123 resolution with 2 × 106 particles is studied to understand the scalability of the proposed methods on parallel machines. We have developed a stable and highly scalable parallel solver with an affordable computational cost even for ill-conditioned systems through preconditioning. On 64 cores, using GMRes in 2D domain decomposition, we achieved a speed-up of ~5.6x (relative to 1D domain decomposition on the same number of processors). Our complexity analysis showed that for large N-body problems, the proposed GMRes scheme scales well for moderate to large number of processors in current tera to petascale computers. © 2013 Elsevier Inc.","year":"2013","title":"Analysis and parallel implementation of a forced N-body problem","volume":"245","pages":"235-258","doi":"10.1016/j.jcp.2013.03.008","journal":"Journal of Computational Physics","bibtex":"@article{10.1016/j.jcp.2013.03.008,\n abstract = \"The understanding of particle dynamics in N-body problems is of importance to many applications in astrophysics, molecular dynamics and cloud/plasma physics where the theoretical representation results in a coupled system of equations for a large number of entities. This paper concerns algorithms for solving a specific N-body problem, namely, a system of disturbance velocities for hydrodynamically interacting particles in a particle-laden turbulent flow. The system is derived from the improved superposition method of [1]. Targeting for scalable computations on petascale computers, we have carried out a thorough study of a parallel implementation of GMRes with different features, such as preconditioners, matrix-free and parallel sparse representation of the matrix through 1D and 2D spatial domain decompositions. Gauss-Seidel method is also studied as a reference iterative algorithm. The range of conditions for efficiency and failure of each method is discussed in detail. Through perturbation analysis, we have conducted a series of experiments to understand the effect of particle sizes, interaction symmetry, inter-particle distances and interaction truncation on the eigenvalues and normality of the linear system. For situations where the system is ill-conditioned, we introduce a restricted Schwarz type preconditioner. We verified the parallel efficiency of the preconditioner using 1D domain decomposition on a parallel machine. A benchmark problem of particle laden turbulence at 5123 resolution with 2 × 106 particles is studied to understand the scalability of the proposed methods on parallel machines. We have developed a stable and highly scalable parallel solver with an affordable computational cost even for ill-conditioned systems through preconditioning. On 64 cores, using GMRes in 2D domain decomposition, we achieved a speed-up of \\textasciitilde 5.6x (relative to 1D domain decomposition on the same number of processors). Our complexity analysis showed that for large N-body problems, the proposed GMRes scheme scales well for moderate to large number of processors in current tera to petascale computers. © 2013 Elsevier Inc.\",\n year = \"2013\",\n title = \"Analysis and parallel implementation of a forced N-body problem\",\n volume = \"245\",\n pages = \"235-258\",\n doi = \"10.1016/j.jcp.2013.03.008\",\n journal = \"Journal of Computational Physics\"\n}\n\n","key":"10.1016/j.jcp.2013.03.008","id":"10.1016/j.jcp.2013.03.008","bibbaseid":"anonymous-analysisandparallelimplementationofaforcednbodyproblem-2013","urls":{},"downloads":0,"html":""},"search_terms":["analysis","parallel","implementation","forced","body","problem"],"keywords":[],"authorIDs":[],"dataSources":["gKiCRHjjC2iGthGEx"]}