Nonstandard Finite Difference Time Domain Algorithm for Berenger’s Perfectly Matched Layer
关键词:
Nonstandard Finite Difference Time Domain Algorithm for Berenger’s Perfectly Matched Layer摘要
The nonstandard (NS) finite difference time domain (FDTD) algorithm provides remark- ably high accuracy on a coarse grid by optimiz- ing to monochromatic wave propagation within each uniform region. But, an effective absorb- ing boundary condition (ABC) is also necessary to accurately calculate electromagnetic fields. Al- though Berenger’s perfectly matched layer (PML) is a highly effective ABC, there is still no NS- formulation of it. In this paper, we develop a NS- version of the PML (NS-PML). We compare the NS-PML with other ABCs and demonstrate its excellent absorption.
##plugins.generic.usageStats.downloads##
参考
R. E. Mickens, “Nonstandard Finite Differ-
ence Models of Differential Equations,” World
Scientific, 1994.
J. B. Cole, “High-Accuracy Yee Algorithm
Based on Nonstandard Finite Differences:
New Developments and Verifications,” IEEE
Trans. Antennas Propag., vol. 50, no. 9, pp.
-1191, 2002.
J. B. Cole, S. Banerjee, and M. I. Haftel,
“High Accuracy Nonstandard Finite Differ-
ence Time-Domain Algorithms for Computa-
tional Electromagnetics: Applications to Op-
tics and Photonics,” chap. 4, pp. 89-109 in
Advances in the Applications of Nonstandard
Finite Difference Schemes, R. E. Mickens,
ed., Scientific, 2005.
N. Okada and J. B. Cole, “Simulation of
Whispering Gallery Modes in the Mie Regime
using the Nonstandard Finite-Difference Time
Domain Algorithm,” J. Opt. Soc. Am. B, vol.
, no. 4, pp. 631-639, 2010.
J. B. Cole and D. Zhu, “Improved Version of
the Second-Order Mur Absorbing Boundary
Condition Based on a Nonstandard Finite Dif-
ference Model,” Applied Computational Elec-
tromagnetic Society (ACES) Journal, vol. 24,
no. 4, pp. 375-381, 2009.
M. F. Hadi, “Wide-Angle Absorbing Bound-
ary Conditions for Low and High-Order
FDTD Algorithms,” Applied Computational
Electromagnetic Society (ACES) Journal, vol.
, no. 1, pp. 9-15, 2009.
J. P. Berenger, “A Perfectly Matched Layer for
the Absorption of Electromagnetic Waves,” J.
Comput. Phys., vol. 114, no. 2, pp. 185-200,
W. C. Chew and J. M. Jin, “Perfectly Matched
Layers in the Discretized Space: An Analysis
ACES JOURNAL, VOL. 26, NO. 2, FEBRUARY 2011
and Optimization,” Electromagnetics, vol. 16,
pp. 325-340, 1996.
Z. Wu and J. Fang, “Numerical Implementa-
tion and Performance of Perfectly Matched
Layer Boundary Condition for Waveguide
Structures,” IEEE Trans. Microwave Theory
Tech., vol. 43, no. 12, pp. 2676-263, 1995.
S. Abarbanel and D. Gottlieb, “A Mathemati-
cal Analysis of the PML Method,” J. Comput.
Phys., vol. 134, no. 2, pp. 357-363, 1997.
F. L. Teixeira and W. C. Chew, “Finite-
Difference Computation of Transient Electro-
magnetic Waves for Cylindrical Geometries
in Complex Media,” IEEE Trans. Geosci. Re-
mote Sens., vol. 38, no. 4, pp. 1530-1543,
R. L. Higdon, “Absorbing Boundary Condi-
tions for Difference Approximations to the
Multi-Dimensional Wave Equation,” Mathe-
matics of Computation, vol. 47, no. 176, pp.
-459, 1986.
W. C. Chew and W. H. Weedon, “A 3D
Perfectly Matched Medium from Modified
Maxwell’s Equations with Stretched Coordi-
nates,” Microwave Optical Tech. Lett., vol. 7,
no. 13, pp. 599-604, 1994.
L. Zhao and A. C. Cangellaris, “A General
Approach for the Development of Unsplit-
Field Time-Domain Implementations of Per-
fectly Matched Layers for FDTD Grid Trun-
cation,” IEEE Microwave and Guided Wave
Letters, vol. 6, no. 5, pp. 209-211, 1996.
S. Wang and F. L. Teixeira, “Some Remarks
on the Stability of Time-Domain Electro-
magnetic Simulations,” IEEE Trans. Antennas
Propag., vol. 52, no. 3, pp. 895-898, 2004.


