Chin. Phys. B Vol. 24, No. 2 (2015) 024101
Uniform stable conformal convolutional perfectly
matched layer for enlarged cell technique conformal
finite-difference time-domain method
∗
Wang Yue(王 玥)
a)
, Wang Jian-Guo(王建国)
a)b)†
, and Chen Zai-Gao(陈再高)
a)b)
a)
Northwest Institute of Nuclear Technology, P. O. Box 69-1, Xi’an 710024, China
b)
School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
(Received 3 May 2014; revised manuscript received 2 July 2014; published online 10 December 2014)
Based on conformal construction of physical model in a three-dimensional Cartesian grid, an integral-based con-
formal convolutional perfectly matched layer (CPML) is given for solving the truncation problem of the open port when
the enlarged cell technique conformal finite-difference time-domain (ECT-CFDTD) method is used to simulate the wave
propagation inside a perfect electric conductor (PEC) waveguide. The algorithm has the same numerical stability as the
ECT-CFDTD method. For the long-time propagation problems of an evanescent wave in a waveguide, several numerical
simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based con-
formal CPML. Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the
open port of the waveguide.
Keywords: enlarged cell technique, conformal, finite-difference time-domain, convolutional perfectly
matched layer
PACS: 41.20.Cv DOI: 10.1088/1674-1056/24/2/024101
1. Introduction
The finite-difference time-domain (FDTD) method has
been proven to be an effective algorithm that provides accu-
rate predictions of field behaviors for various electromagnetic
interaction problems.
[1]
Unfortunately, in its original formula-
tion with orthogonal meshes, the method does not provide a
good accuracy when curved surfaces are present. The earli-
est way of addressing the problem of curved surfaces was to
use staircase approximations. Although trivially simple, this
method is known to introduce errors, which remain there even
when the mesh size is very small.
[2]
An alternative approach to
the problem is to use locally distorted meshes where the basic
Cartesian grids are modified only in the vicinity of the metal
boundaries. One such a scheme, i.e., the contour path FDTD
(CP-FDTD) scheme,
[3–6]
is formulated in terms of the inte-
gral form of Maxwell’s equations instead of the usual differ-
ential form. A major advantage of this approach, when com-
pared with other conformal techniques, is that the simplicity
and efficiency of the Cartesian mesh are retained throughout
the majority of the problem space and only those nodes ad-
jacent to the curved surface need to be specially investigated.
However, the time step size of CP-FDTD scheme must be re-
duced to ensure stability, owing to the presence of small ir-
regular cells near the boundary. To solve the time step re-
duction problem, an enlarged cell technique conformal FDTD
(ECT-CFDTD) method is introduced.
[7,8]
In the ECT-CFDTD
method, the small irregular cells near the material interface are
enlarged into their adjacent cells to ensure stability, even at the
maximum time step of the CFL condition for the conventional
FDTD method.
When the ECT-CFDTD method is used to simulate the
wave propagation in a passive waveguide device, the confor-
mal truncation of the open boundary of the waveguide cannot
be avoided. In this paper, we discuss the truncation technique
that is used in the ECT-CFDTD method.
In 1994, Berenger proposed the split-field perfectly
matched layer absorbing media,
[9]
which introduced an arti-
ficial lossy tensor with both electric and magnetic conductivi-
ties for decaying the electromagnetic waves. This method was
proven to be the most efficient technique for the truncation of
FDTD lattices at that time,
[9–14]
and it has been widely used
since then. Nevertheless, a limitation of the PML formula-
tions that are commonly used is that they are ineffective for
absorbing evanescent waves. As a result, the simulation re-
gion must be set to be large enough so that the evanescent
waves are sufficiently decayed, which widely reduces the ca-
pability of the numerical simulation. In 1996, Kuzuolog and
Mittra introduced a strictly causal form of the PML by sim-
ply shifting the frequency-dependent pole off the real axis and
into the negative-imaginary half of complex plane.
[15]
This
is named the complex frequency shifted PML (CFS-PML). It
has been shown that the CFS-PML is highly efficient for ab-
sorbing the evanescent waves with a long time history. Un-
fortunately, this method is very complicated to implement in
∗
Project supported by the National Natural Science Foundation of China (Grant No. 61231003).
†
Corresponding author. E-mail: wanguiuc@mail.xjtu.edu.cn
© 2015 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn
024101-1