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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, 2-3-1 Matsukadai Higashi-ku, Fukuoka 813-8503, Japan,

tsuyoshi@ieee.org

2Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime 790–8577 Japan,

mmayumi@dpc.ehime-u.ac.jp

3Fukuoka Institute of Technology, 3-30-1 Wajiro-higashi Higashi-ku Fukuoka 811-0295

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 data-rate 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 2D-TM 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

finite-difference 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 Type-M 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, Grant-in-Aid for Young

Scientists (B)(20760251, 2008).

References

[1] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference

Time-Domain 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. 556-593, 2001.

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−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

[3] K. Okubo and N. Takeuchi, ”Analysis of an Electromagnetic Field Created by Line Cur-

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[5] Y. Ando and M. Hayakawa, ”Implementation of the Perfect Matched Layer to the CIP

Method,” IEICE Trans. Electron., vol. 89-C, no. 5, pp. 645–648, 2006.

[6] T. Matsuoka, M. Matsunaga, and T. Matsunaga, ”An Analysis of the Electromagnetic

Waves Radiated from a Line Source which is Close to a Concrete Wall by using the CIP

Method,” IEEJ Trans. Fundamentals and Material, vol. 128-A, no. 2, pp. 53-58, 2008. (in

Japanese)

[7] M. Koga, J. Sonoda, and M. Sato, ”Characteristics of Numerical Dispersion Error of the

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