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2015-07-08
Improvement of Computational Performance of Implicit Finite Difference Time Domain Method
By
Progress In Electromagnetics Research M, Vol. 43, 1-8, 2015
Abstract
Different solution techniques, computational aspects and the ways to improve the performance of 3D frequency dependent Crank Nicolson finite difference time domain (FD-CN-FDTD) method are extensively studied here. FD-CN-FDTD is an implicit unconditionally stable method allowing time discretization beyond the Courant-Friedrichs-Lewy (CFL) limit. For the solution of the method both direct and iterative solver approaches have been studied in detail in terms of computational time, memory requirements and the number of iteration requirements for convergence with different CFL numbers (CFLN). It is found that at higher CFLN more iterations are required to converge resulting in increased number of matrix-vector multiplications. Since matrix-vector multiplications account for the most significant part of the computations their efficient implementation has been studied in order to improve the overall efficiency. Also the scheme has been parallelized in shared memory architecture using OpenMP and the resulted improvement of performance at different CFLN is presented. It is found that better speed-up due to parallelization always comes at higher CFLN implying that the use of FD-CN-FDTD method is more appropriate while parallelized.
Citation
Hasan Khaled Rouf , "Improvement of Computational Performance of Implicit Finite Difference Time Domain Method," Progress In Electromagnetics Research M, Vol. 43, 1-8, 2015.
doi:10.2528/PIERM15052402
http://www.jpier.org/PIERM/pier.php?paper=15052402
References

1. Taflove, A. and S. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd Ed., Artech House, Boston, MA, 2005.

2. Yang, Y., R. Chen, and E. Yung, "The unconditionally stable Crank Nicolson FDTD method for three-dimensional Maxwell’s equations," Microwave and Optical Technology Letters, Vol. 48, 1619-1622, 2006.
doi:10.1002/mop.21684

3. Rouf, H. K., F. Costen, and S. G. Garcia, "3-D Crank-Nicolson finite difference time domain method for dispersive media," Electronics Letters, Vol. 45, No. 19, 961-962, 2009.
doi:10.1049/el.2009.1940

4. 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.
doi:10.1163/156939309790109261

5. Joseph, R., S. Hagness, and A. Taflove, "Direct time integration of Maxwell’s equations in line dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses," Optics Letters, Vol. 16, No. 18, 1412-1414, 1991.
doi:10.1364/OL.16.001412

6. Crank, J. and P. Nicolson, "A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type," Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 43, 50-67, 1947.
doi:10.1017/S0305004100023197

7. Barrett, R., et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM Press, Philadelphia, 1993.

8. Saad, Y. and M. H. Schultz, "GMRES: A generalized minimal residual method for solving nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, Vol. 7, 856-869, 1986.
doi:10.1137/0907058

9. Van der Vorst, H., "BiCGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems," SIAM Journal on Scientific and Statistical Computing, Vol. 13, 631-644, 1992.
doi:10.1137/0913035

10. Yang, Y., et al., "Application of iterative solvers in 3D Crank-Nicolson FDTD method for simulating resonant frequencies of the dielectric cavity," Asia-Pacific Microwave Conference, 1-4, 2007.

11. Numerical Analysis Group, , Rutherford Appleton Laboratory Harwell Subroutine Library, (HSL), 2007 for Researchers, http://www.hsl.rl.ac.uk/hsl2007/hsl20074researchers.html.

12. Saad, Y., "SPARSKIT: A basic toolkit for sparse matrix computations (Version 2),", Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994, http://www-users.cs.umn.edu/ saad/software/SPARSKIT/sparskit.html.

13. Rouf, H. K., "Unconditionally stable finite difference time domain methods for frequency dependent media,", Ph.D. Thesis, The University of Manchester, UK, 2010.

14. Rouf, H. K., F. Costen, and M. Fujii, "Modelling EM wave interactions with human body in frequency dependent Crank Nicolson method," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 17-18, 2429-2441, 2011.
doi:10.1163/156939311798806185

15. Chandra, R., et al., Parallel Programming in OpenMP, Morgan Kaufmann, 2001.