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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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. Google Scholar

Prof. Qunsheng Cao

Prof. Xinlei Chen