A new set of symplectic operators for the symplectic multi-resolution time-domain (S-MRTD) method is obtained by using the time reversible constraint and the growth factor. Then, the perfectly matched layer absorbing boundary condition based on splitting field technique is introduced into the S-MRTD method and its iterative formula is derived. The stability and numerical dispersion of S-MRTD method with optimised symplectic operators are discussed in detail. Finally, the optimal S-MRTD method is applied to the calculation of electromagnetic radiation and scattering. Numerical calculation and simulation results show that the S-MRTD is more accurate and efficient than the traditional FDTD method.

References

1. 1)
  - 10. Hirono, T., Lui, W., Seki, S., et al: ‘A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator’, IEEE Trans. Microw. Theory Tech., 2001, 49, (9), pp. 1640–1648.
2. 2)
  - 15. Sun, Z., Shi, L.H., Zhang, X., et al: ‘Multiresolution time domain scheme using symplectic integrators’, Prog. Electromagn. Res. M, 2013, 32, pp. 1–11.
3. 3)
  - 12. Sha, W., Huang, Z., Chen, M., et al: ‘Survey on symplectic finite-difference time-domain schemes for Maxwell's equations’, IEEE Trans. Antennas & Propag., 2008, 56, (2), pp. 493–500.
4. 4)
  - 8. Represa, C., Pereira, C., Cabeceira, A.C.L., et al: ‘PML absorbing boundary conditions for the multiresolution time-domain techniques based on the discrete wavelet transform’, Appl. Comp. Electro. Soc. (ACES) J., 2005, 20, (3), pp. 207–212.
5. 5)
  - 11. Kusaf, M., Oztoprak, A.Y., Daoud, D.S., et al: ‘Optimized exponential operator coefficients for symplectic FDTD method’, IEEE Microw. Wirel. Compon. Lett., 2005, 15, (2), pp. 86–88.
6. 6)
  - 4. Li-Hua, W., Xian-Liang, W.U., Kai-Hong, S., et al: ‘Stability and numerical dispersion of RK-MRTD schemes’, J. Anhui Univ.(Nat. Sci. Ed.), 2011, 35, (5), pp. 68–72.
7. 7)
  - 2. Zhang, J., Chen, Z.: ‘An unconditionally stable 3-D ADI-MRTD method free of the CFL stability condition’, IEEE Microw. Wirel. Compon. Lett., 2001, 11, (8), pp. 349–351.
8. 8)
  - 13. Guo, Z., Lin, D.: ‘Application of the PML absorbing boundary condition to FD-TD simulation’, J. Electron. (China), 1998, 15, (2), pp. 168–173.
9. 9)
  - 6. Wei, M., Huang, Z., Wu, B., et al: ‘A novel symplectic multi-resolution time-domain scheme for electromagnetic simulations’, IEEE Microw. Wirel. Compon. Lett., 2013, 23, (4), pp. 175–177.
10. 10)
  - 1. Krumpholz, M., Katehi, L.P.B.: ‘New time-domain schemes based on multiresolution analysis’, IEEE Trans. Microw. Theory Tech., 1996, 44, (4), pp. 555–571.
11. 11)
  - 9. Zhixiang, H., Wei, S., Xianliang, W.U.: ‘Scheme of symplectic FDTD’, Syst. Eng. Electron., 2009, 31, (2), pp. 456–458.
12. 12)
  - 3. Cao, Q., Kanapady, R., Reitich, F., et al: ‘High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics’, IEEE Trans. Microw. Theory Tech., 2006, 54, (8), pp. 3316–3326.
13. 13)
  - 14. Song, H., Yang, H.W.: ‘Analysis of numerical dispersion properties of SFDTD and MRTD schemes’, Optik – Int. J. Light and Electron Opt., 2012, 123, (3), pp. 272–275.
14. 14)
  - 7. Berenger, J.P.: ‘Three-dimensional perfectly matched layer for the absorption of electromagnetic waves’, J. Comput. Phys., 1996, 127, (2), pp. 363–379.
15. 15)
  - 5. Min, W., Xian-Liang, W.U., Zhi-Xiang, H., et al: ‘The scheme of symplectic MRTD using propagation technique’, Acta Electron. Sin., 2012, 40, (5), pp. 1034–1038.

Symplectic MRTD for solving three-dimensional Maxwell equations based on optimised operators

References

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