Analysis of Wave Propagation in a Concrete Building Model by the CIP Method

Conference Paper: A Measurement Method of Electrical Parameters of Dielectric Materials by Using Cylindrical Standing Waves
Proceedings of the 2009 International Symposium on Antennas and Propagation; 01/2009
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Analysis of Wave Propagation in a Concrete
Building Model by the CIP Method
Tsuyoshi Matsuoka1,#Mayumi Matsunaga2, Toshiaki Matsunaga3
1Kyushu Sangyo University, 231 Matsukadai Higashiku, Fukuoka 8138503, Japan,
tsuyoshi@ieee.org
2Ehime University, 3 Bunkyocho, Matsuyama, Ehime 790–8577 Japan,
mmayumi@dpc.ehimeu.ac.jp
3Fukuoka Institute of Technology, 3301 Wajirohigashi Higashiku Fukuoka 8110295
Japan, matunaga@fit.ac.jp
Introduction1
The computer simulation of electromagnetic (EM) wave propagation in time domain plays
an important role of development of wireless communications. Higher frequency is required for
high datarate communication; it makes the simulation large scale computation. Up to now,
the FDTD method have been widely used for the computer simulation[1]. Recently, another
method, the constrained interpolation profile (CIP) method, which had been developed in
hydrodynamics [2], has been utilized for the analysis of EM wave propagation [3, 4, 5, 6].
The CIP method has been thought an attractive numerical technique which can analyze
EM wave propagation. The method is not necessary to give any absorbing boundary condition
in general. The CIP method might obtain relatively accurate results compared with the FDTD
method when the available memory size are the same[3]. The dispersion characteristics of the
CIP method has shown to be better in phase but worse in amplitude than those of the FDTD
method[7]. Therefore the CIP method has some better characteristics than the FDTD method.
In addition to theoretical evaluation, it is necessary to evaluate the CIP method experimentally
from practical point of view.
This paper presents a study to verify the effectiveness of the CIP method for analysis
of electromagnetic wave propagation in 2D structure from experimental point of view. The
structure is a typical model of a concrete building which consists of passage with a cross
junction and concrete partitions. The electromagnetic waves from a line source located in
the passage are numerically analyzed by the CIP method and the results are compared with
not only those analyzed by the FDTD method but also the measurement data obtained by
experiment using a scale model. These comparisons show the effectiveness of the CIP method
for analyzing the electromagnetic waves propagation in the 2D structures experimentally.
2Analysis of EM wave propagation by the CIP method
2.1 Brief explanation of the CIP method
The CIP method is one of the numerical solver for the following advection equations.
∂W
∂t
in which W is a function of x and t, and u is assumed to be constant for simplicity. In this
case, the spatial derivative of the W, ∂xW =∂W
W and ∂xW after ∆t time step are obtained by W(x−u∆t) and ∂xW(x−u∆t), respectively.
Therefore the profile of W and ∂xW are important for the computer simulation of eqn. (1).
In the CIP method, W and ∂xW are assigned at each grid point to numerically compute the
eqn. (1). Then the profile of W between grid points can be interpolated by cubic polynomials
and considered to be approximated precisely[2].
+ u∂W
∂x
= 0 (1)
∂x, also obeys the same advection equation; the
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2.2 Application of the CIP method to EM problem
Consider the 2DTM wave (Ey,Hx,Hz) propagation in a isotropic and homogeneous medium
where permittivity, permeability, electric and magnetic conductivity are assumed to be ε(=
εrε0), µ(= µrµ0), σ and σ∗, respectively. The ε0and µ0are permittivity and permeability of
vacuum, respectively. In the medium, Maxwell’s equation can be reduced to the following form
by applying the normalization of ey=√εEy,hx=√µHxand hz=√µHz.
hz
−vc
where vc=
ting technique and performing some operations, the eqn. (2) becomes the following equations.
[
[
∂
∂t
hz
∂
∂t
ey
hx
=
√εµ. To solve the eqn. (2) by the CIP method, by introducing the directional split
∂
∂x
0
0
0
0
0
−vc
0
0
·
ey
hx
hz
+∂
∂z
0
vc
0
vc
0
0
0
0
0
·
ey
hx
hz
−
σ
εey
σ∗
µhx
σ∗
µhz
(2)
1
∂
∂t
W+
W−
x
x
]
]
+
∂
∂x
[
[
vc
0
0
−vc
]
]
[
·
[
[
hx
W+
W−
x
x
]
]
=
(
(
−σ
2ε
)[
)[
]
ey
−ey
]
]
+
(
(
−σ∗
2µ
)[
)[
hz
hz
]
]
(3)
∂
∂t
W+
W−
z
z
+∂
∂z
vc
0
0
−vc
·
W+
W−
]
z
z
=
−σ
[
2ε
−ey
ey
+
−σ∗
2µ
hx
hx
(4)
= −σ∗
2µ
hx
hz
(5)
in which W±
∂W
∂α= g (α = x,z). The inhomogeneous equation can be solved by the following steps; first,
homogeneous equations∂W
finitedifference method is applied to∂W
In addition, another calculation is required in the multidimensional analysis of the CIP
method. In the calculation of α direction, the Wαand ∂αWαat the next time step are obtained
by the CIP method while ∂βWαis not, where α,β = x,z. In this paper, a conventional upwind
scheme is used for ∂βWαpropagating in the α direction; it is called TypeM CIP method [3].
If the absorbing boundary characteristics within the CIP method scheme is not sufficient,
the perfect matched layer (PML) is easily introduced into this scheme; the σ and σ∗in the
PML are chosen to satisfy the impedance matching.
The treatment of the boundary between different media and the current source are described
in the reference [3, 4].
x = hz± ey and W±
z = hx∓ ey. The eqn (3) and (4) have the form of
∂W
∂t±
∂t±∂W
∂α= 0 are solved by the CIP method and then a conventional
∂t= g.
3Numerical Analysis and Experimental Setup
The geometry of the problem is shown in Fig. 1. A line source which produces a sinusoidal
wave with operating frequency 10 GHz is located at (x,z) = (0,−14.17λ). The λ is the
wavelength in the vacuum. The parameters used in calculation are as follows. The grid size
are ∆x = ∆z =
is 54λ × 54λ and the PML with 1.6 λ is provided outside the domain. The width of concrete
partitions T is 1.5λ, and the width of passages W1and W2are 5.0λ and 6.67λ, respectively.
The EM fields and their spatial derivative are assigned at each grid point and the medium
parameters between the grid points are assumed to be constant.
Concrete partition is regarded as a homogeneous medium with εr = 6.0,µr = 1,σ =
0.052,σ∗= 0.0. The rest of the computational domain is lossless medium with εr= µr= 1.
The σ in the PML is σi = σ0(
counted from the boundary of computational domain and Npml is the number of cells in
the PML. In the numerical calculation, The DFT is performed to obtain field distribution.
λ
40, and the Courant number c = 0.2. The dimension of computational domain
i
Npml)2, σ0 = 0.477, σ∗
i= σiµ
ε, where i is the cell number
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z
y
0
W1
Source
54λ
54λ
14.17λ
Concrete
εr=6.0
σ=0.052 S/m
x
W1
W1
T
W2
εr=1.0, µr=1.0
Figure 1: The geometry of the problem
The model as shown in fig 1 has been
made by some concrete blocks with thick
ness of 10mm on a aluminium plate and
covered by other aluminium plates with
slots for probe. Therefore the blocks have
been sandwiched by aluminum plates; 2D
model can be realized based on the image
theory. The experimental data have been
averaged at each measurement point.
4
and Experimental Results
Comparison of Numerical
For the comparison with numerical
and experimental results, the numerical
data have been normalized by each max
imum value of the Eyon the z axis. The
experimental data have been scaled to be
fitted to the numerical data at near the line source.
Figure 2 shows the comparison of the results by the CIP method and those by experiment.
For reference, the results obtained by FDTD method are also depicted in the same figures. The
figures show that results of the CIP and FDTD methods are good agreement each other in the
region of line of sight and of z < −4λ while we can see small differences between both results
in the rest of the region. The comparisons of numerical and experimental results illustrate
that the results of the CIP method agree with experimental ones as well as those of the FDTD
method do.
5 Conclusion
This paper has presented the analysis of the electromagnetic wave propagation in a typ
ical model of concrete building by using the CIP method. The experiments have been also
performed by using a scale model. The CIP method has given the almost the same results
with those analyzed by the FDTD method. In addition, the CIP method have given the
good agreement results with the experimental ones. These results have indicated that the CIP
method can be applicable and effective to the analysis of wave propagation in 2D structure
from experimental point of view.
Acknowledgments
This work was partially supported by the Strategic Information and Communications R &
D Promotion Programme (SCOPE) from the Ministry of Internal Affairs and Communications
of Japan, and the Ministry of Education, Science, Sports and Culture, GrantinAid for Young
Scientists (B)(20760251, 2008).
References
[1] A. Taflove and S. C. Hagness, Computational Electrodynamics: The FiniteDifference
TimeDomain Method 3rd. Ed., Artech House, 2005.
[2] T. Yabe, F. Xiao, and T. Utsumi, ”The constrained interpolation profile method for
multiphase analysis,” J. Comm. Phys., vol. 169, no. 2, pp. 556593, 2001.
Page 4
−20020
−60
−40
−20
0
z/λ
Ey [dB]
f=10 [GHz]
εr=6.0
σ=0.052 [S/m]
Measured
CIP method
FDTD
(a) z/λ on z axis
−200 20
−60
−40
−20
0
x/λ
Ey [dB]
f=10 [GHz]
εr=6.0
σ=0.052 [S/m]
Measured
CIP method
FDTD
(b) x/λ on x axis
−20020
−60
−40
−20
0
Ey [dB]
z/λ
f=10 [GHz]
εr=6.0
σ=0.052 [S/m]
Measured
CIP method
FDTD
(c) z/λ along z axis on x = 5λ
−200 20
−60
−40
−20
0
Ey [dB]
z/λ
f=10 [GHz]
εr=6.0
σ=0.052 [S/m]
Measured
CIP method
FDTD
(d) z/λ along the z axis on x = 12.3λ
Figure 2: Comparison of Ey obtained by the CIP and FDTD methods with experimental
results : (a) , (b) on x axis, (c) along z axis on x=5λ, (d) along z axis on x=12.3λ
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[5] Y. Ando and M. Hayakawa, ”Implementation of the Perfect Matched Layer to the CIP
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