Vol. 128
Latest Volume
All Volumes
PIER 180 [2024] PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2012-05-31
Finite Element Matrix Generation on a GPU
By
Progress In Electromagnetics Research, Vol. 128, 249-265, 2012
Abstract
This paper presents an efficient technique for fast generation of sparse systems of linear equations arising in computational electromagnetics in a finite element method using higher order elements. The proposed approach employs a graphics processing unit (GPU) for both numerical integration and matrix assembly. The performance results obtained on a test platform consisting of a Fermi GPU (1x Tesla C2075) and a CPU (2x twelve-core Opterons), indicate that the GPU implementation of the matrix generation allows one to achieve speedups by a factor of 81 and 19 over the optimized single-and multi-threaded CPU-only implementations, respectively.
Citation
Adam Dziekonski, Piotr Sypek, Adam Lamecki, and Michal Mrozowski, "Finite Element Matrix Generation on a GPU," Progress In Electromagnetics Research, Vol. 128, 249-265, 2012.
doi:10.2528/PIER12040301
References

1. Shahmansouri, A. and B. Rashidian, "GPU implementation of split-field finite-difference time-domain method for Drude-Lorentz dispersive media," Progress In Electromagnetics Research, Vol. 125, 55-77, 2012.
doi:10.2528/PIER12010505

2. Gao, P. C., Y. B. Tao, Z. H. Bai, and H. Lin, "Mapping the SBR and TW-ILDCs to heterogeneous CPU-GPU architecture for fast computation of electromagnetic scattering," Progress In Electromagnetics Research, Vol. 122, 137-154, 2012.
doi:10.2528/PIER11092303

3. Gao, P. C., Y. B. Tao, and H. Lin, "Fast RCS prediction using multiresolution shooting and bouncing ray method on the GPU," Progress In Electromagnetics Research, Vol. 107, 187-202, 2010.
doi:10.2528/PIER10061807

4. Banasiaka, R., Z. Yeb, and M. Soleimanic, "Improving three-dimensional electrical capacitance tomography imaging using approximation error model theory," Journal of Electromagnetic Waves and Applications, Vol. 26, No. 2-3, 411-421, 2012.

5. Jiang, W.-Q., M. Zhang, and Y. Wang, "CUDA-based radiative transfer method with application to the EM scattering from a two-layer canopy model," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 17-18, 2509-2521, 2010.
doi:10.1163/156939310793675772

6. Sadiku, M. N. O., Numerical Techniques in Electromagnetics, 2nd Edition, CRC, 2000.
doi:10.1201/9781420058277

7. Fotyga, G., K. Nyka, and M. Mrozowski, "Effcient model order reduction for FEM analysis of waveguide structures and resonators," Progress In Electromagnetics Research, Vol. 127, 277-295, 2012.
doi:10.2528/PIER12021609

8. Klopf, E. M., S. B. Manic, M. M. Ilic, and B. M. Notaros, "Effcient time-domain analysis of waveguide discontinuities using higher order FEM in frequency domain," Progress In Electromagnetics Research, Vol. 120, 215-234, 2011.

9. Trujillo-Romero, C. J., L. Leija, and A. Vera, "FEM modeling for performance evaluation of an electromagnetic oncology deep hyperthermia applicator when using monopole, inverted T, and plate antennas," Progress In Electromagnetics Research, Vol. 120, 99-125, 2011.

10. Sun, H., Y. Wu, and Z. Ruan, "Edge-Based finite element method analysis of the transmission characteristics in antipodal finline," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 4, 565-575, 2011.
doi:10.1163/156939311794500250

11. Sun, H., Y. Wu, and Z. Ruan, "A study of transmission characteristics in elliptic-shaped microshield lines," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 17-18, 2353-2364, 2011.
doi:10.1163/156939311798806176

12. Jin, J., The Finite Element Method in Electromagnetics, John Wiley and Sons Inc., New York, 2002.

13. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics. Antennas, Microwave Circuits and Scattering Applications, IEEE Series on Electromagnetic Wave Theory, IEEE Press, NJ, 1998.

14. Pelosi, G., R. Coccioli, and S. Selleri, Quick Finite Elements for Electromagnetic Waves, Artech House Inc., 2009.

15. Dehnavi, M. M., D. M. Fernandez, and D. Giannacopoulos, "Finite-element sparse matrix vector multiplication on graphic processing unit," IEEE Transactions on Magnetics, Vol. 46, No. 8, 2982-2985, Aug. 2010.
doi:10.1109/TMAG.2010.2043511

16. Dziekonski, A., A. Lamecki, and M. Mrozowski, "A memory effcient and fast sparse matrix vector product on a GPU," Progress In Electromagnetics Research, Vol. 116, 49-63, Jan.2011.

17. Dziekonski, A., A. Lamecki, and M. Mrozowski, "GPU acceleration of multilevel solvers for analysis of microwave components with finite element method," IEEE Microwave and Wireless Components Letters, Vol. 21, No. 1, 1-3, 2011.
doi:10.1109/LMWC.2010.2089974

18. Dziekonski, A., A. Lamecki, and M. Mrozowski, "Tuning a hybrid GPU-CPU V-Cycle multilevel preconditioner for solving large real and complex systems of FEM equations," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 619-622, 2011.
doi:10.1109/LAWP.2011.2159769

19. Plaszewski, P., K. Banas, and P. Maciol, "Higher order FEM numerical integration on GPUs with OpenCL," Proceedings of the International Multiconference on Computer Science and Information Technology (IMCSIT), 337-34, Oct. 18-20,2010.

20. Maciol, P., P. Plaszewski, and K. Banas, "3D finite element numerical integration on GPUs," Procedia Computer Science, Vol. 1, No. 1, 1093-1100, 2010.
doi:10.1016/j.procs.2010.04.121

21. Markall, G., A. Slemmer, D. Ham, P. Kelly, C. Cantwell, and S. Sherwin, "Finite element assembly strategies on multi-core and many-core architectures," International Journal for Numerical Methods in Fluids, 2012.

22. Cecka, C., A. Lew, and E. Darve, "Application of assembly of finite element methods on graphics processors for real-time elastodynamics," GPU Gems 3, Jul. 2011.

23. Ingelstrom, P., "A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes," IEEE Trans. on Microwave Theory and Techniques, Vol. 54, 106-114, Jan.2006.
doi:10.1109/TMTT.2005.860295

24. Zhang, L., T. Cui, and H. Liu, "A set of symmetric quadrature rules on triangles and tetrahedra," Journal of Computational Mathematics, Vol. 26, No. 3, 1-16, 2008.

25. Schberl, J., "NETGEN an advancing front 2D/3D-mesh generator based on abstract rules," Computing and Visualization in Science, Vol. 1, No. 1, 41-52, Jul.1997.

26. Sanders, J. and E. Kandrot, CUDA by Example: An Introduction to General-Purpose GPU Programming, NVIDIA Co., 2011.

27. http://www.nvidia.com/content/PDF/fermi..

28., CUBLAS Library Nvidia Co., 2011.

29. Saad, Y., Iterative Methods for Sparse Linear Systems,SIAM, 2004.

30. http://software.intel.com/en-us/articles/intel-mkl/.

31., CUDA CUSPARSE Library, NVIDIA Co.,2011.

32. http://www.cise.ufledu/research/sparse/umfpack..