Productivity of a low-budget computer cluster applied to overcome the n-body problem

• Autorzy: Nowicki Tomasz , Gregosiewicz Adam , Łagodowski Zbigniew

Identyfikatory

DOI

10.23743/acs-2021-32

• Języki publikacji: EN

Abstrakty

EN

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 pre-sented research included writing original computer code, building a computer cluster, preforming simulations and comparing the results.

Słowa kluczowe

EN

computer clusters; parallel computing; n-body problem

PL

klastry komputerowe; obliczenia równoległe; problem n-body

• Wydawca: Polskie Towarzystwo Promocji Wiedzy ; Lublin University of Technology
• Czasopismo: Applied Computer Science
• Rocznik: 2021
• Tom: Vol. 17, no 4
• Strony: 100--109
• Opis fizyczny: Bibliogr. 14 poz., fig., tab.

Twórcy

autor

Nowicki Tomasz

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

• https://orcid.org/0000-0003-0752-2509

autor

Gregosiewicz Adam

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

• https://orcid.org/0000-0002-6702-8505

autor

Łagodowski Zbigniew

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

• https://orcid.org/0000-0003-1811-6151

Bibliografia

• [1] 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
• [2] Cottet, G. H., & Koumoutsakos, P. D. (2000). Vortex Methods Theory and Practice. Cambridge University Press.
• [3] 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
• [4] 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
• [5] Hockney, R. W., & Eastwood, J. W. (1988). Computer Simulation Using Particles. Taylor & Francis Group.
• [6] 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
• [7] 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
• [8] 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
• [9] Lewis, R. I. (1991). Vortex Element Methods for Fluid Dynamics of Engineering Systems. Cambridge University Press.
• [10] 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
• [11] Nowicki, T. (2012). Wpływ sposobu realizacji warunków brzegowych w metodzie wirów dyskretnych na odpowiedź aeroelastyczną pomostów. Politechnika Lubelska.
• [12] 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
• [13] 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
• [14] 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.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).