PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 58 > pp. 101-114

IMPLEMENTATION OF MUR'S ABSORBING BOUNDARIES WITH PERIODIC STRUCTURES TO SPEED UP THE DESIGN PROCESS USING FINITE-DIFFERENCE TIME-DOMAIN METHOD

By G. Zheng, A. A. Kishk, A. W. Glisson, and A. B. Yakovlev

Full Article PDF (254 KB)

Abstract:
The finite-difference time-domain (FDTD) method is used to obtain numerical solutions of infinite periodic structures without resorting to the complex frequency-domain analysis, which is required in traditional frequency-domain techniques. The field transformation method is successfully used to model periodic structures with oblique incident waves/scan angles. Maxwell's equations are transformed so that only a single period of the infinite periodic structure is modeled in FDTD by using periodic boundary conditions (PBCs). When modeling periodic structures with the transformed fields, the standard Mur second-order absorbing boundary condition cannot be used directly to absorb the outgoing waves. This paper presents a new implementation of Mur's second-order absorbing boundary condition (ABC) with the transformed fields in the FDTD method. For designs that require multi-parametric studies, Mur's ABCs are efficient and sufficient boundary conditions. If more accurate results are needed, the perfectly matched layer (PML) ABC can be used with the parameters obtained from the Mur solution.

Citation: (See works that cites this article)
G. Zheng, A. A. Kishk, A. W. Glisson, and A. B. Yakovlev, "Implementation of Mur's Absorbing Boundaries with Periodic Structures to Speed Up the Design Process Using Finite-Difference Time-Domain Method," Progress In Electromagnetics Research, Vol. 58, 101-114, 2006.
doi:10.2528/PIER05062103
http://www.jpier.org/PIER/pier.php?paper=0506213

References:
1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antenn. Propagat., Vol. AP-14, No. 3, 302-307, 1966.

2. Engquist, B. and A. Ma jda, "Absorbing boundary conditions for the numerical simulation of waves," Math. Comp., Vol. 31, No. 139, 629-651, 1977.
doi:10.2307/2005997

3. Mur, G., "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., Vol. EMC-23, No. 4, 377-382, 1981.

4. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnet waves," J. Comput. Phys., Vol. 114, 185-200, 1994.
doi:10.1006/jcph.1994.1159

5. Munk, B. A., Frequency Selective Surfaces: Theory and Design, John Wiley, 2000.

6. Yablonovitch, E., "Photonic band-gap structures," J. Opt. Soc. Amer. B., Vol. 10, No. 2, 283-294, 1993.

7. Maloney, J. G. and M. P. Kesler, "Analysis of antenna arrays using the split-field update FDTD method," Proc. IEEE AP-S Int. Symp., Vol. 4, 2036-2039, 1998.

8. Veysoglu, M. E., R. T. Shin, and J. A. Kong, "A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incident case," J. Electromagnetic Waves and Applications, Vol. 7, No. 12, 1595-1607, 1993.

9. Kao, Y. C. A. and R. G. Atkins, "A finite difference-time domain approach for frequency selective surfaces at oblique incidence," Proc. IEEE AP-S Int. Symp., Vol. 2, 1432-1435, 1996.

10. Kao, Y. C. A., "Finite-difference time domain modeling of oblique incidence scattering from periodic surfaces," Thesis, 1997.

11. Roden, J. A., "Electromagnetic analysis of complex structures using the FDTD technique in general curvilinear coordinates," Ph.D. Thesis, 1997.

12. Roden, J. A., S. D. Gedney, M. P. Kesler, J. G. Maloney, and P. H. Harms, "Time-domain analysis of periodic structures at oblique incidence: Orthogonal and nonorthogonal FDTD implementations," IEEE trans. Microwave Theory and Techniques, Vol. 46, 420-427, 1998.
doi:10.1109/22.664143

13. Harms, P. H., J. A. Roden, J. G. Maloney, M. P. Kesler, E. J. Kuster, and S. D. Gedney, "Numerical analysis of periodic structures using the split-field algorithm," Proc. 13th Annual Review of Progress in Applied Computational Electromagnetics, 104-111, 1997.

14. Taflove, A. and S. C. Hagness, Computational Electromagnetics: the Finite-Difference Time-Domain Method, 2nd ed., Artech House, Norwood, 2000.


© Copyright 2014 EMW Publishing. All Rights Reserved