volume | PIER Journals

Abstract

We incorporate high-order symplectic time integrators into multiresolution time domain (MRTD) schemes. The stability and numerical dispersion analysis are presented. The proposed scheme preserves the symplectic structure of Maxwell's equations and can be easily implemented in program codes. Compared to Runge-Kutta (RK)-MRTD, the suggested scheme is more accurate in long-term simulations and requires less computational resource.

1. Sanz-Serna, J. M. and M. P. Calvo, Numerical Hamiltonian Problems, Chapman & Hall, London, UK, 1994.

2. Hirono, T., W. Lui, S. Seki, and Y. Yoshikuni, "A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator," IEEE Trans. on Microw. Theory and Tech., Vol. 49, 1640-1648, 2001.
doi:10.1109/22.942578

3. Sha, W., Z. Huang, M. Chen, and X. Wu, "Survey on symplectic finite-difference time-domain scheme for Maxwell's equation," IEEE Trans. on Antennas and Propag., Vol. 56, No. 2, 493-500, 2008.
doi:10.1109/TAP.2007.915444

4. Sha, W., Z. Huang, X. Wu, and M. Chen, "Application of the symplectic finite-difference time-domain scheme to electromagnetic simulation," J. Comput. Phys., Vol. 225, 33-50, 2007.
doi:10.1016/j.jcp.2006.11.027

5. Sha, W., X. Wu, Z. Huang, and M. Chen, "Waveguide simulation using the high-order symplectic finite-difference time-domain scheme," Progress In Electromagnetics Research B, Vol. 13, 237-256, 2009.
doi:10.2528/PIERB09012302

6. Kusaf, M., A. Y. Oztoprak, and D. S. Daoud, "Optimized exponential operator coefficients for symplectic FDTD method," IEEE Microw. Wireless Compon. Lett.,, Vol. 15, No. 2, 86-88, 2005.
doi:10.1109/LMWC.2004.842827

7. Gradoni, G., V. Mariani Primiani, and F. Moglie, "Reverberation chamber as a multivariate process: FDTD evaluation of correlation matrix and independent positions," Progress In Electromagnetics Research, Vol. 133, 217-234, 2013.

8. Izadi, M., M. Z. A. Ab Kadir, and C. Gomes, "Evaluation of electromagnetic fields associated with inclined lightning channel using second order FDTD-hybrid methods," Progress In Electromagnetics Research, Vol. 117, 209-236, 2011.

9. Vaccari, A., A. Cala' Lesina, L. Cristoforetti, and R. Pontalti, "Parallel implementation of a 3D subgridding FDTD algorithm for large simulations," Progress In Electromagnetics Researc, Vol. 120, 263-292, 2011.

10. Krumpholz, M. and L. P. B. Katehi, "MRTD: New time-domain schemes based on multiresolution analysis," IEEE Trans. on Microwave Theory and Tech., Vol. 44, No. 4, 555-571, 1996.
doi:10.1109/22.491023

11. Liu, Y., Y.-W. Chen, P. Zhang, and X. Xu, "Implementation and application of the spherical MRTD algorithm," Progress In Electromagnetics Research, Vol. 139, 577-597, 2013.

12. Sarris, C. D., "New concepts for the multiresolution time domain (MRTD) analysis of microwave structures," Proc. 34th Eur. Microw. Conf., Vol. 2, 881-884, London, UK, 2004..

13. Cao, Q., R. Kanapady, and F. Reitich, "High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics," IEEE Trans. on Microw. Theory and Tech., Vol. 54, No. 8, 3316-3326, 2006.
doi:10.1109/TMTT.2006.879130

14. Chen, X. and Q. Cao, "Analysis of characreristics of two-dimensional Runge-Kutta multiresolution time-domain scheme," Progress In Electromagnetics Research M, Vol. 13, 217-227, 2010.

15. Fujii, M. and W. J. R. Hoefer, "Dispersion of time-domain wavelet-Galerkin method based on Daubechies compactly supported scaling functions with three and four vanishing moments," IEEE Microwave Guided Wave Lett., Vol. 10, No. 4, 125-127, 2000.
doi:10.1109/75.846920

Dr. Zheng Sun

Dr. Li-Hua Shi

Dr. Xiang Zhang

Dr. Yinghui Zhou