volume | PIER Journals

Abstract

In this paper the stability condition of the Runge-Kutta m-order multiresolution time-domain (RKm-MRTD) scheme has been studied. By analyzing the amplification factors, we derive the numerical dispersion relation of the RK-MRTD scheme. The numerical dispersive and dissipative errors are investigated. Finally, the theoretical predictions of the numerical errors are calculated through the numerical simulations.

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

2. Cao, Q., Y. Chen, and R. Mittra, "Multiple image technique (MIT) and anisotropic perfectly matched layer (APML) in implementation of MRTD scheme for boundary truncations of microwave structures," IEEE Trans. Microw. Theory Tech., Vol. 50, No. 6, 1578-1589, Jun. 2002.
doi:10.1109/TMTT.2002.1006420

3. Zhu, X., T. Dogaru, and L. Carin, "Analysis of the CDF biorthogonal MRTD method with application to PEC targets," IEEE Trans. Microw. Theory Tech., Vol. 51, No. 9, 2015-2022, Sep. 2003.
doi:10.1109/TMTT.2003.815874

4. Alighanbari, A. and C. D. Sarris, "Dispersion properties and applications of the Coifman scaling function based S-MRTD," IEEE Trans. Antennas and Propagation, Vol. 54, No. 8, 2316-2325, Aug. 2006.
doi:10.1109/TAP.2006.879194

5. Gottlieb, S., C.-W. Shu, and E. Tadmor, "Strong stability-preserving high-order time discretization methods," SIAM Rev., Vol. 43, No. 1, 89-112, 2001.
doi:10.1137/S003614450036757X

6. Chen, M.-H., B. Cockburn, and F. Reitich, "High-order RKDG methods for computational electromagnetics," J. Sci. Comput., Vol. 22-23, No. 1-3, 205-226, Jun. 2005.
doi:10.1007/s10915-004-4152-6

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

8. Liu, Y., "Fourier analysis of numerical algorithms for the Maxwell's equations," J. Comput. Phys., Vol. 124, 396-416, 1996.
doi:10.1006/jcph.1996.0068

9. Yefet, A. and P. G. Petropoulos, "A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations," Sci. Eng., Tech. Rep., Inst. Comput. Applicat, NASA/CR-1999n-209n514, 1999.

10. Shan, Z. and G. W. Wei, "High-order FDTD methods via derivative matching for Maxwell's equations with material interface," J. Comput. Phys., Vol. 200, No. 1, 60-103, Oct. 2004.

11. Sun, G. and C. W. Trueman, "Analysis and numerical experiments on the numerical dispersion of two-dimensional ADI-FDTD," IEEE Antenna and Wireless Propagation Lett., Vol. 2, No. 7, 78-81, 2003.

Prof. Qunsheng Cao

Prof. Xinlei Chen