PRODUCTIVITY OF A LOW-BUDGET COMPUTER CLUSTER APPLIED TO OVERCOME THE N-BODY PROBLEM

Tomasz NOWICKI

t.nowicki@pollub.pl
Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Computer Science (Poland)

Adam GREGOSIEWICZ


Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics (Poland)

Zbigniew ŁAGODOWSKI


Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics (Poland)

Abstract

The classical n-body problem in physics addresses the prediction of individual motions of a group of celestial bodies under gravitational forces and has been studied since Isaac Newton formulated his laws. Nowadays the n-body problem has been recognized in many more fields of science and engineering. Each problem of mutual interaction between objects forming a dynamic group is called as the n-body problem. The cost of the direct algorithm for the problem is O(n2) and is not acceptable from the practical point of view. For this reason cheaper algorithms have been developed successfully reducing the cost to O(nln(n)) or even O(n). Because further improvement of the algorithms is unlikely to happen it is the hardware solutions which can still accelerate the calculations. The obvious answer here is a computer cluster that can preform the calculations in parallel. This paper focuses on the performance of a low-budget computer cluster created on ad hoc basis applied to n-body problem calculation. In order to maintain engineering valuable results a real technical issue was selected to study. It was Discrete Vortex Method that is used for simulating air flows. The presented research included writing original computer code, building a computer cluster, preforming simulations and comparing the results.


Keywords:

computer clusters, parallel computing, n-body problem

Aparinov, A. A., & Setukha, A. V. (2009). On the application of mosaic-skeleton approximations of matrices for the acceleration of computations in the vortex method for the three-dimensional Euler equations. Differential Equations, 45, 1358. http://doi.org/10.1134/S0012266109090110
DOI: https://doi.org/10.1134/S0012266109090110   Google Scholar

Cottet, G. H., & Koumoutsakos, P. D. (2000). Vortex Methods Theory and Practice. Cambridge University Press. Dynnikova, G. Ya. (2009). Fast technique for solving the N-body problem in flow simulation by vortex methods. Computational Mathematics and Mathematical Physics, 49, 1389–1396. http://doi.org/10.1134/S0965542509080090
DOI: https://doi.org/10.1134/S0965542509080090   Google Scholar

Groen, D., Zwart, S. P., Ishiyama, T., & Makino, J. (2011). High Performance Gravitational N-body Simulations on a Planet-wide Distributed Supercomputer. Computational Science & Discovery, 4(1), 015001. http://doi.org/10.1088/1749-4699/4/1/015001
DOI: https://doi.org/10.1088/1749-4699/4/1/015001   Google Scholar

Hockney, R. W., & Eastwood, J. W. (1988). Computer Simulation Using Particles. Taylor & Francis Group.
DOI: https://doi.org/10.1201/9781439822050   Google Scholar

Huang, M. J., Su, H. X., & Chen, L. Ch. (2009). A fast resurrected core-spreading vortex method with no-slip boundary conditions. Journal of Computational Physics, 228(6), 1916–1931. https://doi.org/10.1016/j.jcp.2008.11.026
DOI: https://doi.org/10.1016/j.jcp.2008.11.026   Google Scholar

Incardona, P., Leo, A., Zaluzhny, Y., Ramaswamy, R., & Sbalzarini, I. F. (2019). OpenFPM: A scalable open framework for particle and particle-mesh codes on parallel computers. Computer Physics Communications, 241, 155–177. https://doi.org/10.1016/j.cpc.2019.03.007
DOI: https://doi.org/10.1016/j.cpc.2019.03.007   Google Scholar

Kuzmina, K., Marchevsky, I., & Moreva, V. (2015). Parallel Implementation of Vortex Element Method on CPUs and GPUs. Procedia Computer Science, 66, 73–82. https://doi.org/10.1016/j.procs.2015.11.010
DOI: https://doi.org/10.1016/j.procs.2015.11.010   Google Scholar

Lewis, R. I. (1991). Vortex Element Methods for Fluid Dynamics of Engineering Systems. Cambridge University Press.
DOI: https://doi.org/10.1017/CBO9780511529542   Google Scholar

Nowicki, T. (2007). Algorytm równoległy dla problemu n-ciał (Unpublished master thesis). Lublin University of Technology, Lublin. https://github.com/TomekNowicki/vorsym/blob/main/nowicki_n-body.pdf
  Google Scholar

Nowicki, T. (2012). Wpływ sposobu realizacji warunków brzegowych w metodzie wirów dyskretnych na odpowiedź aeroelastyczną pomostów. Politechnika Lubelska.
  Google Scholar

Nowicki, T. (2015). The Discrete Vortex Method for estimating how surface roughness affects aerodynamic drag acting on a long cylinder exposed to wind. Technical Transactions, Civil Engineering, 2-B(12), 127–144. https://doi.org/10.4467/2353737XCT.15.129.4166
  Google Scholar

Ricciardi, T. R., Wolf, W. R., & Bimbato, A. M. (2017). A fast algorithm for simulation of periodic flows using discrete vortex particles. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 4555–4570. http://doi.org/10.1007/s40430-017-0902-x
DOI: https://doi.org/10.1007/s40430-017-0902-x   Google Scholar

Ricciardi, T., R., Bimbato, A. M., Wolf, W., R., Idelsohn, S. R., Sonzogni, V., Coutinho, A., Cruchaga, M., Lew, A., & Cerrolaza, M. (2015). Numerical simulation of vortex interactions using a fast multipole discrete particle method. Proceedings Of The 1st Pan-american Congress On Computational Mechanics And Xi Argentine Congress On Computational Mechanics (pp. 1065–1076). Barcelona: Int Center Numerical Methods Engineering.
  Google Scholar

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Published
2021-12-30

Cited by

NOWICKI, T., GREGOSIEWICZ, A., & ŁAGODOWSKI, Z. (2021). PRODUCTIVITY OF A LOW-BUDGET COMPUTER CLUSTER APPLIED TO OVERCOME THE N-BODY PROBLEM. Applied Computer Science, 17(4), 100–109. https://doi.org/10.23743/acs-2021-32

Authors

Tomasz NOWICKI 
t.nowicki@pollub.pl
Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Computer Science Poland

Authors

Adam GREGOSIEWICZ 

Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics Poland

Authors

Zbigniew ŁAGODOWSKI 

Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics Poland

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