The programmable graphics processing unit (GPU) is employed to accelerate the unconditionally stable Crank-Nicolson finite-difference time-domain (CN-FDTD) method for the analysis of microwave circuits. In order to efficiently solve the linear system from the CN-FDTD method at each time step, both the sparse matrix vector product (SMVP) and the arithmetic operations on vectors in the bi-conjugate gradient stabilized (Bi-CGSTAB) algorithm are performed with multiple processors of the GPU. Therefore, the GPU based BI-CGSTAB algorithm can significantly speed up the CN-FDTD simulation due to parallel computing capability of modern GPUs. Numerical results demonstrate that this method is very effective and a speedup factor of 10 can be achieved.
"GPU Accelerated Unconditionally Stable Crank-Nicolson FDTD Method for the Analysis of Three-Dimensional Microwave Circuits," Progress In Electromagnetics Research,
Vol. 102, 381-395, 2010. doi:10.2528/PIER10020606
1. Yee, K. S., "Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. 14, No. 8, 302-307, Aug. 1966.
2. Sun, G. and C. W. Trueman, "Unconditionally stable Crank-Nicolson scheme for solving the two-dimensional Maxwell's equations," IEE Electron. Lett., Vol. 39, No. 7, 595-597, Apr. 2003.
3. Sun, G. and C. W. Trueman, "Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TE waves," EEE Trans. Antennas Propagat., Vol. 52, No. 11, 2963-2972, Nov. 2004.
4. Yang, Y., R. S. Chen, D. X. Wang, , and E. K. N. Yung, "Unconditionally stable Crank-Nicolson finite-difference time-domain method for simulation of 3-D microwave circuits," IEE Microwaves, Antennas & Propagation, Vol. 1, No. 4, 937-942, Aug. 2007.
5. Rouf, H. K., F. Costen, S. G. Garcia, and S. Fujino, "On the solution of 3-D frequency dependent Crank-Nicolson FDTD scheme," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 16, 2163-2175, 2009.
6. Van der Vorst, H. A., "Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems," SIAM J. Sci. Statist. Comput., Vol. 13, No. 2, 631-644, Mar. 1992.
7. Zhang, S. L., "GPBi-CG: Generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems," SIAM J. Sci. Comput., Vol. 18, No. 2, 537-551, Mar 1997.
8. Owens, J. D., M. Houston, et al. "GPU computing," Proceedings of the IEEE, Vol. 96, No. 5, 879-899, May 2008.
9. Krakiwsky, S. E., , L. E. Turner, and M. M. Okoniewski, "Acceleration of finite-difference time-domain (FDTD) using graphics processor units (GPU)," IEEE MTT-S Int. Microwave Symp. Digest, 1033-1036, 2004.
10. Inman, M. J. and A. Z. Elsherbeni, "Programming video cards for computational electromagnetics applications," Antennas Propag. Mag., Vol. 47, 71-78, Dec. 2005.
11. Zainud-Deen, S. H.., E. El-Deen, et al. "Electromagnetic scattering using gpu-based finite difference frequency domain method," Progress In Electromagnetics Research B, Vol. 16, 351-369, 2009.
12. Tao, Y. B., H. Lin, and H. J. Bao, "From CPU to GPU: GPU-based electromagnetic computing (GPUECO)," Progress In Electromagnetics Research, Vol. 81, 1-19, 2008.
13. Peng, S. X. and Z. P. Nie, "Acceleration of the method of moments calculations by using graphics processing units," IEEE Trans. Antennas and Propagation, Vol. 56, No. 7, 2130-2133, Jul. 2008.
15. Mur, G., "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagmetic-field equations," IEEE Trans. Electromagnetic Compatibility, Vol. 23, No. 4, 377-382, Nov. 1981.
16. Gibson, W. C., The Method of Moments in Electromagnetics, Chapman & Hall/CRC, 2007.
17. Bracken, J. E., D. K. Sun, and Z. J. Cendes, "S-domain methods for simultaneous time and frequency characterization of electromagnetic devices," IEEE Trans. Microwave Theory Tech., Vol. 46, 1277-1290, Sep. 1998.
18. Sheen, D. M., S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the three-dimensional finite-difference time-domain method to the analysis of planar microstrip circuits," IEEE Trans. Microwave Theory Tech., Vol. 38, 849-857, Jul. 1990.
19. Maricevic, Z. A. and T. K. Sarkar, "Analysis and measurements of arbitrarily shaped open microstrip structures," Progress In Electromagnetics Research, Vol. 15, 253-301, 1997.