Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 2: results and their evaluation

• Autorzy: Gołębiowski J. , Forenc J.
• Języki publikacji: EN

Abstrakty

EN

Using models and algorithms presented in the first part of the article, a spatio-temporal distribution of the step response of a floor heater was determined. The results have been presented in the form of heating curves and temperature profiles of the heater in the selected time moments. The computations results were verified through comparing them with the solution obtained with the use of a commercial program - NISA. Additionally, the distribution of the average time constant of thermal processes occurring in the heater was determined. The analysis of the use of a graphics processing unit in numerical computations based on the conjugate gradient method was done. It was proved that the use of a graphics processing unit is profitable in the case of solving linear systems of equations with dense coefficient matrices. In the case of a sparse matrix, the speed-up depends on the number of its non-zero elements.

Słowa kluczowe

EN

air floor heating; step response computation; parallel computations; GPGPU

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2013
• Tom: Vol. 61, nr 4
• Strony: 949--954
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr., tab.

Twórcy

autor

Gołębiowski J.

• Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Białystok, Poland

autor

Forenc J.

• Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Białystok, Poland

Bibliografia

• [1] J. Gołębiowski and J. Forenc, “Parallel computations of the step response of a floor heater with the use of a graphics processing unit. Part 1: models and algorithms”, Bull. Pol. Ac.: Tech. 61 (4), 943-948 (2013).
• [2] Compute Unified Device Architecture (CUDA), http://www.nvidia.com/object/cudahomenew.html (2012).
• [3] D.B. Kirk and W.W. Hwu, Programming Massively Parallel Processors: a Hands-on Approach, Morgan Kaufmann, Burlington, 2010.
• [4] CUDA CUBLAS Library, NVIDIA Corporation, Santa Clara, CA, 2010.
• [5] CUDA CUSPARSE Library, NVIDIA Corporation, Santa Clara, CA, 2010.
• [6] Manuals for NISA v. 16. NISA Suite of FEA Software (CDROM), Cranes Software, Inc., Troy, Michigan, 2008.
• [7] J. Gołębiowski and S. Kwiećkowski, “Dynamics of threedimensional temperature field in electrical system of floor heating”, Int. J. Heat Mass Tran. 45 (12), 2611-2622 (2002).
• [8] W. Lipiński and J. Gołębiowski, “Modelling of electromagnetic shield dynamics”, IEEE Trans. on Magnetics 16 (6), 1419-1422 (1980).
• [9] J.D. Hoffman, Numerical Methods for Engineers and Scientists, Marcel Dekker Inc., New York, 2001.
• [10] S. Rosłoniec, Fundamental Numerical Methods for Electrical Engineering, Springer-Verlag, Berlin, 2008.
• [11] J.R. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain”, in Technical Report, Carnegie Mellon University, Pittsburgh, 1994.
• [12] V. Jalili-Marandi and V. Dinavahi, “SIMD-based large-scale transient stability simulation on the graphics processing unit”, IEEE Trans. on Power Systems 25 (3), 1589-1599 (2010).
• [13] Intel Math Kernel Library. Reference Manual, MKL 10.3 Update 10, Intel Corporation, 2012.
• [14] J. Dongarra, “Basic linear algebra subprograms technical forum standard”, Int. J. High Performance Computing Applications 16 (1), 1-111 (2002).
• [15] R. Barrett, M. Berry, T.F. Chan, J. Demmel, J.M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, Ch. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994.
• [16] J. Forenc, “Determination of the initial conditions in the parallel method for the state equation solving”, Electronics and Telecommunications Q. 54 (3), 277-288 (2008).
• [17] J. Gołębiowski and R.P. Bycul, “Thermal analysis of shortcircuit and cooling states in a DC cable with the use of parallel computations”, Electrical Review 85 (10), 95-100 (2009).
• [18] M. Naumov, “Incomplete-LU and Cholesky preconditioned iterative methods using CUSPARSE and CUBLAS”. White Paper, NVIDIA Corporation, London, 2011.
• [19] W.A. Wiggers, V. Bakker, A.B.J. Kokkeler, and G.J.M. Smit, “Implementing the conjugate gradient algorithm on multi-core systems”, Proc. Int. Symp. on System-on-Chip 1, 11-14 (2007).
• [20] L. Buatois, G. Caumon, and B. Levy, “Concurrent number cruncher: a GPU implementation of a general sparse linear solver”, Int. J. Parallel Emerg. Distrib. Syst. 24 (3), 205-223 (2009).
• [21] A. Cevahir, A. Nukada, and S. Matsuoka, “Fast conjugate gradients with multiple GPUs”, Lecture Notes in Computer Science 5544, 893-903 (2009).
• [22] M. Ament, G. Knittel, D. Weiskopf, and W. Straser, “A parallel preconditioned conjugate gradient solver for the poisson problem on a Multi-GPU platform”, Proc. Euromicro Int. Conf. on Parallel, Distributed and Network-Based Computing 1, 583-592 (2010).
• [23] R. Helfenstein and J. Koko, “Parallel preconditioned conjugate gradient algorithm on GPU, J. Comp. Appl. Math. 236, 3584-3590 (2012).