Wide-Angle Absorbing Boundary Conditions for Low and High-Order FDTD Algorithms
Keywords:
Wide-Angle Absorbing Boundary Conditions for Low and High-Order FDTD AlgorithmsAbstract
Wide-angle performance of the perfectlymatched- layer absorbing boundary conditions for the finite-difference time-domain (FDTD) method is investigated for efficient modeling of electrically large structures. The original split-field, uniaxial and convolutional perfectly-matched-layer formulations are all optimized to produce near-flat absorption for incidence angles up to 87 degrees. Optimized wide-angle parameters are derived for both the standard FDTD method and a high-order finite-volumes-based variant. The investigated high-order algorithm in particular is shown to produce improved wide-angle performance over standard FDTD for all three perfectly-matched-layer variants even when they are optimized for normal wave incidence. In all cases, optimization is managed through appropriate choices of modeling parameters which can be directly and unobtrusively applied to existing FDTD codes.
Downloads
References
J. Fang, “Time domain finite difference computa-
tion for Maxwell’s equations,” Ph.D. dissertation,
University of California at Berkeley, Berkeley, CA,
M. F. Hadi and M. Piket-May, “A modified FDTD
(2,4) scheme for modeling electrically large struc-
tures with high-phase accuracy,” IEEE Trans. An-
tennas Propagat., vol. 45, no. 2, pp. 254–264, Feb.
E. Turkel and A. Yefet, “Fourth order method for
Maxwell’s equations on a staggered mesh,” vol. 4,
pp. 2156–2159, Jul. 1997.
J. B. Cole, “A high-accuracy realization of the
Yee algorithm using non-standard finite differences,”
IEEE Trans. Microwave Theory Tech., vol. 45, no. 6,
pp. 991–996, Jun. 1997.
J. L. Young, D. Gaitonde, and J. S. Shang, “Toward
the construction of a fourth-order difference scheme
for transient EM wave simulation: Staggered grid
approach,” IEEE Trans. Antennas Propagat., vol. 45,
no. 11, pp. 1573–1580, Nov. 1997.
G. J. Haussmann, “A dispersion optimized three-
dimensional finite-difference time-domain method
for electromagnetic analysis,” Ph.D. dissertation,
University of Colorado at Boulder, Boulder, CO,
N. V. Kantartzis and T. D. Tsiboukis, “A higher-
order FDTD technique for the implementation of
enhanced dispersionless perfectly matched layers
combined with efficient absorbing boundary condi-
tions,” IEEE Trans. Magn., vol. 34, no. 5, pp. 2736–
, Sep. 1998.
Y. W. Cheong, Y. M. Lee, K. H. Ra, J. G.
Kang, and C. C. Shin, “Wavelet-Galerkin scheme
of time-dependent inhomogeneous electromagnetic
problems,” IEEE Microwave Guided Wave Lett.,
vol. 9, no. 8, pp. 297–299, Aug. 1999.
E. A. Forgy and W. C. Chew, “A time-domain
method with isotropic dispersion and increased sta-
bility on an overlapped lattice,” IEEE Trans. Anten-
nas Propagat., vol. 50, no. 7, pp. 983–996, Jul. 2002.
H. E. Abd El-Raouf, E. A. El-Diwani, A. Ammar,
and F. El-Hefnawi, “A low-dispersion 3-D second-
order in time fourth-order in space FDTD scheme
(m3d24),” IEEE Trans. Antennas Propagat., vol. 52,
no. 7, pp. 1638–1646, Jul. 2004.
M. F. Hadi, “A finite volumes-based 3-D low dis-
persion FDTD algorithm,” IEEE Trans. Antennas
Propagat., vol. 55, no. 8, Aug. 2007.
M. F. Hadi and R. K. Dib, “Eliminating inter-
face reflections in hybrid low-dispersion FDTD al-
gorithms,” Appl. Computat. Electromag. Soc. J.,
vol. 22, no. 3, pp. 306–314, Nov. 2007.
——, “Phase-matching the hybrid FV24/S22 FDTD
algorithm,” Progress in Electromagnetics Research,
vol. 72, pp. 307–323, 2007.
A. M. Shreim and M. F. Hadi, “Integral PML
absorbing boundary conditions for the high-order
M24 FDTD algorithm,” Progress in Electromagnet-
ics Research, vol. 76, pp. 141–152, 2007.
J.-P. B ́erenger, “A perfectly matched layer for the
absorption of electromagnetic waves,” Journal of
Computational Physics, vol. 114, no. 2, pp. 185–
, 1994.
W. C. Chew and W. H. Weedon, “A 3D perfectly
matched medium from modified Maxwell’s equa-
tions with stretched coordinates,” Microwave Opt.
Technol. Lett., vol. 7, no. 13, pp. 599–604, Sep.
Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-
F. Lee, “A perfectly anisotropic absorber for use
as an absorbing boundary condition,” IEEE Trans.
Antennas Propagat., vol. 43, no. 12, pp. 1460–1463,
Dec. 1995.
S. D. Gedney, “An anisotropic perfectly matched
layer-absorbing medium for the truncation of FDTD
lattices,” IEEE Trans. Antennas Propagat., vol. 44,
no. 12, pp. 1630–1639, Dec. 1996.
M. Kuzuoglu and R. Mittra, “Frequency dependence
of the constitutive parameters of causal perfectly
matched anisotropic absorbers,” IEEE Microwave
Guided Wave Lett., vol. 6, no. 12, pp. 447–449, Dec.
J. A. Roden and S. D. Gedney, “Convolution PML
(CPML): An efficient FDTD implementation of the
CFS-PML for arbitrary media,” Microwave Opt.
Technol. Lett., vol. 27, no. 5, pp. 334–339, Dec.
J.-P. B ́erenger, “Numerical reflection from FDTD-
PMLs: A comparison of the split PML with the
unsplit and CFS PML,” IEEE Trans. Antennas Prop-
agat., vol. 50, no. 3, pp. 258–265, Mar. 2002.
S. C. Winton and C. M. Rappaport, “Specifying
PML conductivities by considering numerical reflec-
tion dependencies,” IEEE Trans. Antennas Propa-
gat., vol. 48, no. 7, pp. 1055–1063, Jul. 2000.
Y. S. Rickard and N. K. Georgieva, “Problem-
independent enhancement of PML ABC for the
FDTD method,” IEEE Trans. Antennas Propagat.,
vol. 51, no. 10, pp. 3002–3006, Oct. 2003.
S. Kim and J. Choi, “Optimal design of PML absorb-
ing boundary conditions for improving wide-angle
reflection performance,” Electron. Lett., vol. 40,
no. 2, pp. 104–105, Jan. 2004.
X. L. Travassos, S. L. Avila, D. Prescott, A. Nicolas,
ACES JOURNAL, VOL. 24, NO. 1, FEBRUARY 2009
and L. Kr ̈ahenb ̈uhl, “Optimal configurations for per-
fectly matched layers in FDTD simulations,” IEEE
Trans. Magn., vol. 42, no. 4, pp. 563–566, Apr. 2006.
N. V. Kantartzis, T. V. Yioultsis, T. I. Kosmanis,
and T. D. Tsiboukis, “Nondiagonally anisotropic
PML: A generalized unsplit wide-angle absorber for
the treatment of the near-grazing effect in FDTD
meshes,” IEEE Trans. Magn., vol. 36, no. 4, pp. 907–
, Jul. 2000.
R. Holland, L. Simpson, and K. Kunz, “Finite-
difference analysis of EMP coupling to lossy dielec-
tric structures,” IEEE Trans. Electromagn. Compat.,
vol. EMC-22, no. 3, pp. 203–209, Aug. 1980.