1
Numerical Simulation of Vector Wave Scattering
From the Target and Rough Surface Composite
Model with 3-D Multilevel UV Method
Fang-Shun Deng, Si-Yuan He, Hai-Tao Chen, Wei-Dong Hu, Wen-Xian Yu, Guo-Qiang Zhu
Abstract- In this paper, numerical simulation of vector wave
scattering from three-dimensional (3-D) target and rough surface
composite model is investigated with 3-D multilevel UV method.
Due to the adoption of RWG basis functions for accurate
modeling of vector current, the oscillation of the interaction
matrix elements brings difficulty to directly apply the UV
decomposition method. Based on the reordering of the
interaction strength and the sampling according to the
characteristics distribution of the interaction, an EM-
interaction-based sampling algorithm is developed for the
accurate reconstruction of the far interaction submatrix with UV
decomposition method. Combined with multilevel division of the
total composite model, the 3-D multilevel UV method
incorporating the new sampling algorithm is developed for vector
wave scattering from 3-D complex target above or on a random
rough surface. The 3-D multilevel UV method yields a complexity
of
(log)ON N
for the setup time of the impedance matrix, the
solve time of the matrix iterative solution and also for the
memory requirements. The accuracy and the efficiency of the 3-D
multilevel UV method is compared and validated with the full
MOM method and the ACA method in the tested cases. Finally,
the applications of a target above or on the rough surface, for
example, a ship on the sea surface, have been accomplished and
analyzed.
Index terms-
target/rough surface, vector wave scattering, fast
method, UV, RWG
I. INTRODUCTION
Electromagnetic scattering from a target above or on a
rough surface has numerous applications in long-range radar
surveillance, oceanic remote sensing, target identification and
target tracking [1-7]. Numerical simulation of the combined
target and rough surface model is complicated by the
interactions between the target and the rough surface
background [1]. Some numerical methods have been
1
developed for 2-D target/rough surface scattering, e.g., the
1
This work is supported by the National Natural Science Foundation of
China under Grant No. 60671040 and the Chinese National High Technology
Research Plan (863 Plan) under Grant No. 2007 AA12Z172
Fang-Shun Deng, Si-Yuan He and Guo-Qiang Zhu are with the School of
Electronic Information, Wuhan University, Wuhan, China, 430079. (email:
dengfs2009@gmail.com)
Hai-Tao Chen is with the Antenna Lab., Wuhan Maritime Communication
Research Institute, Wuhan, post-Box 70005,China
Wei-Dong Hu is with the ATR Lab., National University of Defense
Technology, Changsha, Hunan, 410073, China
Wen-Xian Yu is with the school of Electronic Information and Electrical
Engineering, Shanghai Jiao Tong University, No. 800 Dongchuan Rd.
Minhang, Shanghai, 200240, China.
forward backward method with spectral acceleration algorithm
(GFBM/SAA) [3], the finite element method (FEM) [4], the
hybrid MOM and PO method [5]. Scattering from 3D
target/rough surface combined model is much more difficult
than the 2-D case because of the large computational
complexity, very few reports have been found for the 3-D case,
e.g. the FDTD method [6], a hybrid KA-MOM algorithm [7].
For the solution of scattering from 3-D composite models,
the application of the traditional MOM method results in a
complicated dense matrix, which causes extremely large
memory requirements and long computation time when the
direct matrix solution is employed. Therefore, the numerical
fast method associated with the iterative solution of the large
matrix equation is very attractive for the solution of the 3-D
composite scattering problems. The bottleneck of the iterative
solution is the calculation of the matrix-vector products, which
still has great complexity for both the time and memory. To
reduce the complexity of the matrix-vector multiplication, the
matrix decomposition techniques [8-13] could be combined in
the iterative steps. According to the matrix decomposition, the
low-ranked far interaction submatrix (
ub
Z
mn×
) between well-
separated regions is compressed into a product of matrix Q
and R (or U and V). Thus the complexity drops from
()Om n
to
(( ))Or m n×+
for both the memory requirement and the CPU
time consumed in matrix vector multiplication of
ub
Z
mn
, where
r
is the rank of
ub
Z
mn
.
The QR matrix decomposition known as IES
3
was first
proposed by Kapur and Long [8] and demonstrated for object
of moderate size. The UV decomposition technique combined
with multilevel partitioning has been applied in the rough
surface scattering problems [9-10]. The compression of the
UV or QR method can be achieved by sampling a little
number of most dominant rows and columns within the
original submatrix. The matrix elements describe the
interaction between the source and field, so from the point of
physics, the sampling procedure is to identify the most
important points, the interactions of which will reconstruct the
entire interaction between the source and field regions. The
successful matrix compression could be assessed in terms of
reconstruction accuracy, compression rate and time efficiency.
A number of sampling algorithms have been developed and
most of them are based on the Gram-Schmidt process [8, 11-
12]. The adaptive cross approximation (ACA) [13] algorithm