volume | PIER Journals

Abstract

In this paper, an efficient time domain simulation algorithm is proposed to analyze the electromagnetic scattering and radiation problems. The algorithm is based on discontinuous Galerkin time domain (DGTD) method and parallelization acceleration technique using the graphics processing units (GPU), which offers the capability for accelerating the computational electromagnetics analyses. The bottlenecks using the GPU DGTD acceleration for electromagnetic analyses are investigated, and potential strategies to alleviate the bottlenecks are proposed. We first discuss the efficient parallelization strategies handling the local-element differentiation, surface integrals, RK time-integration assembly on the GPU platforms, and then, we explore how to implement the DGTD method on the Compute Unified Device Architecture (CUDA). The accuracy and performance of the DGTD method are analyzed through illustrated benchmarks. We demonstrate that the DGTD method is better suitable for GPUs to achieve significant speedup improvement over modern multi-core CPUs.

1. Jin, J., The Finite Element Method in Electromagnetics, 2nd Ed., John Wiley & Sons, 2002.

2. Taflove, A. and S. Hagness, Computational Electromagnetics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, 2005.

3. Peterson, A. and R. Mittra, Computational Methods for Electromagnetics, Wiley-IEEE Press, 1997.
doi:10.1109/9780470544303

4. Yu, W., R. Mittra, X. Yang, et al. Parallel Finite Difference Time Domain Method, Artech House, 2006.

5. Yu, W., Y. Rahmat-Samii, and A. Elsherbeni, Advanced Computational Electromagnetic Methods and Applications, Artech House, 2015.

6. Yee, K., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, 302-307, 1966.
doi:10.1109/TAP.1966.1138693

7. Hesthaven, J. and T. Warburton, Nodal Discontinuous Galerkin Methods, Algorithms, Analysis, and Applications, Springer, 2008.

8. Chen, J. and Q. Liu, "Discontinuous Galerkin time-domain methods for multiscale electromagnetic simulations: A review," Proceeding of The IEEE, Vol. 101, No. 2, 242-254, 2013.
doi:10.1109/JPROC.2012.2219031

9. Jin, J., From FETD to DGTD for Computational Electromagnetics, ACES 2015 Tutorial, March 22-26, 2015.

10. Niegemann, J., Introduction to Computational Electromagnetics The Discontinuous Galerkin Time-Domain (DGTD) Method, Technical Report, Lab for Electromagnetic Fields and Microwave Electronics (IFH), 2012.

11. Busch, K., M. Konig, and J. Niegemann, "Discontinuous Galerkin methods in nanophotonics," Laser Photonics Rev., Vol. 5, No. 6, 773-809, 2011.
doi:10.1002/lpor.201000045

12. Tobon, L. E., Q. Ren, Q. Sun, J. Chen, and Q. H. Liu, "New efficient implicit time integration method for DGTD applied to sequential multidomain and multiscale problems," Progress In Electromagnetics Research, Vol. 151, 1-8, 2015.
doi:10.2528/PIER14112201

13. Yan, S. and J.-M. Jin, "Theoretical formulation of a time-domain finite element method for nonlinear magnetic problems in three dimensions (invited paper)," Progress In Electromagnetics Research, Vol. 153, 33-55, 2015.
doi:10.2528/PIER15091005

14. Shankara, V., A. Mohammadiana, and W. Halla, "A time-domain, finite-volume treatment for the Maxwell equations," Electromagnetics, Vol. 10, No. 1, 127-145, 1990.
doi:10.1080/02726349008908232

15. Karypis, G. and V. Kumar, "Parallel multilevel k-way partition scheme for irregular graphs," SIAM Rev., Vol. 41, No. 2, 278-300, 1999.
doi:10.1137/S0036144598334138

16. Godel, N., 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., Vol. 46, No. 8, 3469-3472, 2010.
doi:10.1109/TMAG.2010.2046022

17. Komatitsch, D., G. Erlebacher, D. Goddeke, and D. Michea, "High-order finite-element seismic wave propagation modeling with MPI large GPU cluster," J. Comput. Phys., Vol. 229, No. 20, 7692-7714, 2010.
doi:10.1016/j.jcp.2010.06.024

18. Komatitsch, D., D. Goddeke, G. Erlebacher, and D. Michea, "Modeling the propagation of elastic waves using spectral elements on a cluster of 192 GPUs," Comput. Sci. Res. Dev., Vol. 25, 75-82, 2010.
doi:10.1007/s00450-010-0109-1

19. Komatitsch, D., D. Michea, and G. Erlebacher, "Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA," J. Parallel Distrib. Comput., Vol. 69, 451-460, 2000.

20. Williamson, J., "Low-storage Runge-Kutta schemes," Journal of Computational Physics, Vol. 35, No. 1, 48-56, 1980.
doi:10.1016/0021-9991(80)90033-9

21. Yang, X. and W. Yu, "PHI coprocessor acceleration techniques for computational electromagnetics methods," ACES Journal, Vol. 29, No. 12, 1013-1016, 2014.

22. Yu, W., X. Yang, and W. Li, VALU, AVX and GPU Acceleration Techniques for Parallel FDTD Methods, SciTech Publishing (An Imprint of the IET), 2014.

23. Shen, J., T. Tang, and L.-L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer, 2011.

24. Van Der Vegt, J. and H. van der Ven, "Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. General formulation," Journal of Computational Physics, Vol. 182, No. 2, 546-585, 2002.
doi:10.1006/jcph.2002.7185

25. NVIDIA CUDA Parallel Programming and Computing Platform, http://www.nvidia.com/object/cuda home new.html.

26. NVIDIA, CUDA C Programming Guide, http://docs.nvidia.com/cuda/cuda-c-programming-guide /index.html#axzz3Yh95qkZB, .

27. POINTWISE, http://www.pointwise.com/apps/.

28. https://www.cst.com/.

29. https://www.feko.info/.

30. http://www.ansys.com/Products/Electronics/ANSYS-HFSS.

Prof. Lei Zhao

Dr. Geng Chen

Dr. Wenhua Yu