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Przyspieszony algorytm analizy pól elektromagnetycznych za pomocą algorytmu SIMD
Języki publikacji
Abstrakty
This article presents a fast Single-Instruction Multiple-Data (SIMD) algorithm that evaluates electromagnetic fields (EMFs). It is based on the Method of Moments (MOM) adapted for execution on an SIMD architecture. The big speed-up obtained with this new implementation enables us to obtain results faster and to simulate more complex and realistic models and keep the computing time within a reasonable range, which give lead to better solutions for current EMF problems. This article gives a brief overview of generic massively parallel processors, taking into consideration their hardware architecture and the new computer languages for managing them. We describe the mathematical foundations of the algorithm in order to explain how the operations are distributed and performed by the GPU. Many cases are simulated to analyze the performance of the method proposed and they are compared with a fully implemented CPU algorithm, as well as with another CPU algorithm that uses the Intel MKL solvers for dense matrices. The differences in performance between floating-point precision numbers and double precision numbers is also studied and how they influence the accuracy of the results. The tests carried out suggest that the acceleration obtained grows with the complexity of the model. As a result, the proposed algorithm’s only limitations lie with the hardware features.
Artykuł przedstawia szybki algorytm typu Single-Instruction Multiple-Data (SIMD - pojedyncza instrukcja wiele danych), do obliczania rozkładu pól elektromagnetycznych (EMF). Jest ona oparta na metodzie momentów (MOM) przystosowanych do realizacji w architekturze SIMD. Duże przyspieszenie uzyskane dzięki tej nowej implementacji pozwala uzyskać wyniki szybciej i dla bardziej złożonych symulacji i realistycznych modeli i utrzymać czas obliczeniowy w rozsądnym zakresie. Artykuł zawiera krótki przegląd procesorów masowo równoległych, biorąc pod uwagę ich architekturę sprzętową i nowe języki programowania do zarządzania nimi. Opisano matematyczne podstawy algorytmu, aby wyjaśnić, w jaki sposób operacje są wykonywane przez procesor graficzny (GPU). Wiele przypadków zostało symulowanych, aby przeanalizować działanie proponowanej metody a wyniki porównano ze znanymi algorytmami, jak również z algorytmem, który wykorzystuje Intel MKL Solvers do gęstych matryc. Z przeprowadzonych testów wynika, że uzyskane przyspieszenie rośnie wraz ze złożonością modelu. Jedyne ograniczenia algorytmu zależą od możliwości sprzętowych.
Wydawca
Czasopismo
Rocznik
Tom
Strony
286--292
Opis fizyczny
Bibliogr. 20 poz., schem., wykr.
Twórcy
autor
- Department of Electrical Engineering, Universidade de Vigo, Lagoas-Marcosende 9, 36310 Vigo, Spain
autor
- Department of Electrical Engineering, Universidade de Vigo, Lagoas-Marcosende 9, 36310 Vigo, Spain
autor
- Department of Electrical Engineering, Universidade de Vigo, Lagoas-Marcosende 9, 36310 Vigo, Spain
autor
- Department of Electrical Engineering, Universidade de Vigo, Lagoas-Marcosende 9, 36310 Vigo, Spain
Bibliografia
- [1] IEEE Standard for Safety Levels With Respect to Human Exposure to Electromagnetic Fields, 0-3 kHz. IEEE Std C95.6-2002, 2002.
- [2] H.-D. Brüns, C. Schuster, and H. Singer. Numerical electromagnetic field analysis for EMC problems. IEEE Trans. Electromagn. Compat., 49(2):253–262, 2007.
- [3] J. Cidrás, A.F. Otero, and C. Garrido. Nodal frequency analysis of grounding systems considering the soil ionization effect. IEEE Trans. Power Del., 15(1):103–107, 2000.
- [4] N. Godel, N. Nunn, T. Warburton, and M. Clemens. Scalability of higher-order discontinuous galerkin FEM computations for solving electromagnetic wave propagation problems on GPU clusters. IEEE Trans. Magn., 46(8):3469–3472, 2010.
- [5] Vehbi C Gungor, Dilan Sahin, Taskin Kocak, Salih Ergut, Concettina Buccella, Carlo Cecati, and Gerhard P Hancke. Smart Grid Technologies: Communication Technologies and Standards. IEEE Trans. Ind. Informat., 7(4):529–539.
- [6] Carl W Hall. Laws and Models: Science, Engineering, and Technology. CRC Press, 1 edition, September 1999.
- [7] JR Humphrey, DK Price, and KE Spagnoli. CULA: hybrid GPU accelerated linear algebra routines. EM Photonics, 2010.
- [8] V Jalili-Marandi and V Dinavahi. SIMD-Based Large-Scale Transient Stability Simulation on the Graphics Processing Unit. Power Systems, IEEE Transactions on, 25(3):1589–1599, 2010.
- [9] M. Kezunovic, Y. Guan, C. Guo, and M. Ghavami. The 21st century substation design: Vision of the future, 2010.
- [10] David B Kirk and Wen-mei W Hwu. Programming Massively Parallel Processors: A Hands-on Approach (Applications of GPU Computing Series). Morgan Kaufmann, 1 edition, February 2010.
- [11] T Nagaoka and S Watanabe. A GPU-based calculation using the three-dimensional FDTD method for electromagnetic field analysis. In Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE, pages 327–330, 2010.
- [12] Hubert Nguyen. GPU Gems 3. Addison-Wesley Professional, August 2007.
- [13] A.F. Otero, J. Cidras, and J.L. del Alamo. Frequency-dependent grounding system calculation by means of a conventional nodal analysis technique. Power Delivery, IEEE Transactions on, 14(3):873–878, 1999.
- [14] Clayton R Paul. Analysis of Multiconductor Transmission Lines. Wiley-IEEE Press, 2 edition, October 2007.
- [15] Jason Sanders and Edward Kandrot. CUDA by Example: An Introduction to General-Purpose GPU Programming. Addison-Wesley Professional, 1 edition, July 2010.
- [16] S L Sobolev and Vladimir L Vaskevich. The Theory of Cubature Formulas (Mathematics and Its Applications (closed)). Springer, softcover reprint of hardcover 1st ed. 1997 edition, February 2011.
- [17] T. Topa, A. Karwowski, and A. Noga. Using GPU with CUDA to accelerate MoM-based electromagnetic simulation of wire-grid models. IEEE Antennas Wireless Propag. Lett., 10:342–345, 2011.
- [18] T. Topa, A. Noga, and A. Karwowski. Adapting MoM with RWG basis functions to GPU technology using CUDA. IEEE Antennas Wireless Propag. Lett., 10:480–483, 2011.
- [19] C Vilacha, A.F. Otero, C. Garrido, and J C Moreira. Magnetic-Field Evaluation in the Vicinity of High-Voltage Electric Systems. Power Delivery, IEEE Transactions on, (99):1, 2012.
- [20] N Whitehead. Precision & Performance: Floating Point and IEEE 754 Compliance for NVIDIA GPUs. NVidia, 2011.
Typ dokumentu
Bibliografia
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