PRODUCTIVITY OF A LOW-BUDGET COMPUTER CLUSTER APPLIED TO OVERCOME THE N-BODY PROBLEM
Tomasz NOWICKI
t.nowicki@pollub.plLublin 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 problemReferences
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
Authors
Tomasz NOWICKIt.nowicki@pollub.pl
Lublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Computer Science Poland
Authors
Adam GREGOSIEWICZLublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics Poland
Authors
Zbigniew ŁAGODOWSKILublin University of Technology, Faculty of Electrical Engineering and Computer Science, Department of Mathematics Poland
Statistics
Abstract views: 295PDF downloads: 30
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in Applied Computer Science are open-access and distributed under the terms of the Creative Commons Attribution 4.0 International License.
Similar Articles
- Nataliya SHABLIY, Serhii LUPENKO, Nadiia LUTSYK, Oleh YASNIY, Olha MALYSHEVSKA, KEYSTROKE DYNAMICS ANALYSIS USING MACHINE LEARNING METHODS , Applied Computer Science: Vol. 17 No. 4 (2021)
- Benjamin KOMMEY, Ernest Ofosu ADDO, Elvis TAMAKLOE, Eric Tutu TCHAO, Henry NUNOO-MENSAH, A SIX-PORT MEASUREMENT DEVICE FOR HIGH POWER MICROWAVE VECTOR NETWORK ANALYSIS , Applied Computer Science: Vol. 18 No. 3 (2022)
- Raphael Olufemi AKINYEDE, Temitayo Elijah BALOGUN, Abiodun Boluwade ROTIMI, Oluwasefunmi Busola FAMODIMU, A CUSTOMER-CENTRIC APPLICATION FOR A CINEMA HOUSE , Applied Computer Science: Vol. 16 No. 2 (2020)
- Krzysztof NIEMIEC, Grzegorz BOCEWICZ, AN AUTHENTICATION METHOD BASED ON A DIOPHANTINE MODEL OF THE COIN BAG PROBLEM , Applied Computer Science: Vol. 20 No. 2 (2024)
- Andrij MILENIN, PARALLEL SOLUTION OF THERMOMECHANICAL INVERSE PROBLEMS FOR LASER DIELESS DRAWING OF ULTRA-THIN WIRE , Applied Computer Science: Vol. 18 No. 3 (2022)
- Błażej BADZIO, Agnieszka BODZIAK, Bartłomiej BRODAWKA, Karol BUCHAJCZUK, Maria SKUBLEWSKA-PASZKOWSKA, Mariusz DZIEŃKOWSKI, Paweł POWROŹNIK, ANALYSIS OF THE USABILITY AND ACCESSIBILITY OF WEBSITES IN VIEW OF THEIR UNIVERSAL DESIGN PRINCIPLES , Applied Computer Science: Vol. 18 No. 3 (2022)
- Raphael Olufemi AKINYEDE, Sulaiman Omolade ADEGBENRO, Babatola Moses OMILODI, A SECURITY MODEL FOR PREVENTING E-COMMERCE RELATED CRIMES , Applied Computer Science: Vol. 16 No. 3 (2020)
- Sylwester KORGA, Marcin BARSZCZ, Krzysztof DZIEDZIC, DEVELOPMENT OF SOFTWARE FOR IDENTIFICATION OF FILAMENTS USED IN 3D PRINTING TECHNOLOGY , Applied Computer Science: Vol. 15 No. 1 (2019)
- Stanisław SKULIMOWSKI, Jerzy MONTUSIEWICZ, Marcin BADUROWICZ, ENHANCING THE EFFICIENCY OF THE LEVENSHTEIN DISTANCE BASED HEURISTIC METHOD OF ARRANGING 2D APICTORIAL ELEMENTS FOR INDUSTRIAL APPLICATIONS , Applied Computer Science: Vol. 19 No. 4 (2023)
- Eduardo Sánchez-García, Javier Martínez-Falcó, Bartolomé Marco-Lajara, Jolanta Słoniec, ANALYZING THE ROLE OF COMPUTER SCIENCE IN SHAPING MODERN ECONOMIC AND MANAGEMENT PRACTICES. BIBLIOMETRIC ANALYSIS , Applied Computer Science: Vol. 20 No. 1 (2024)
You may also start an advanced similarity search for this article.