使用自适应交叉近似算法快速计算导电物体的双站雷达散射截面
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"快速计算导电物体的双站雷达截面(RCS)使用自适应交叉近似算法"
本文探讨了一种高效计算导电物体双站雷达截面(RCS)的方法，该方法基于自适应交叉近似(ACA)算法。自适应交叉近似是一种常见的矩阵压缩技术，常用于分析电磁辐射和散射问题。在远场区域，通过ACA方法对阻抗矩阵进行压缩，然后利用等效偶极子矩方法(EDM)加速填充提取出的阻抗矩阵。在近场区域，采用矩方法或等效偶极子矩方法填充阻抗矩阵。
在计算过程中，文章提出了一种迭代近场预条件技术，用于解决矩阵方程，从而实现RCS的快速计算。这种方法的关键优势在于显著提高了计算效率，同时在不牺牲太多精度的前提下，减少了计算复杂性。论文中提供的数值结果证实了应用该方法可以有效地优化计算性能。
具体来说，ACA算法首先通过对大型阻抗矩阵进行近似，降低存储需求和计算负担。接着，EDM在远场计算中的应用，通过简化模型来减少计算时间，它能够快速地填充压缩后的阻抗矩阵。而在近场，由于散射特性的复杂性，通常需要采用更精确的矩方法或EDM来处理，这两种方法能够精确地描述物体表面的电流分布。
迭代近场预条件技术则是为了进一步提高求解速度。这种技术通过在迭代过程中优化近场的处理，使得矩阵方程的求解更为高效，降低了迭代次数，从而节省了计算时间。
该研究提出了一种结合ACA、EDM以及迭代近场预条件技术的综合策略，对于解决大尺寸导电物体的RCS计算问题具有重要的实用价值。通过这种方式，不仅能够实现快速计算，还能保持计算结果的准确性，对于电磁仿真和雷达系统设计等领域具有显著的工程意义。
999
Fast calculation of bistatic RCS for conducting
objects using the adaptive cross approximation
algorithm
Lei Chen
#1
, Yufa Sun
#2
, Shuaishuai Yang
#3
#
Key Lab. of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University
Hefei, P.R. China
1
546502218cl@sina.com
2
yfsun@ahu.edu.cn
3
yangshuai918@yahoo.com.cn
Abstract— Adaptive cross approximation (ACA) algorithm as a
kind of common matrix compression method is often used to
analyze the electromagnetic radiation and scattering problems.
In the region of far field, the impedance matrix is compressed by
ACA method, and the extracted impedance matrix is accelerated
filling by equivalent dipole-moment method (EDM). In the area
of near field, the method of moments or the equivalent
dipole-moment method is applied for filling the impedance
matrix. The iterative near field preconditioning technique is used
to solve matrix equation, so that fast calculation of radar cross
section (RCS) can be achieved. Numerical results show that the
computational efficiency is improved significantly via applying
the presented method in this paper without sacrificing much
accuracy.
Keywords—
adaptive cross approximation algorithm; equivalent
dipole-moment method; near field preconditioning; radar cross
section
I. INTRODUCTION
With the development of computational electromagnetics,
method of moments (MOM) [1] as a representative of the
integral equation methods has been widely applied to the
analysis of the electromagnetic scattering problems. The
method owns a wide application range and produces higher
calculation accuracy. But with the electric size of the object
increasing, the consumption of the memory and time has
synchronously increased dramatically. Therefore, we usually
adopt matrix compression method to save memory and
computing time, in order to calculate the RCS easily. At
present, the main methods of matrix compression include
single IE-QR [2] method, UV multilevel partitioning method
[3] and multi-layer matrix decomposition algorithm (MLMDA)
[4], etc. This paper introduces a kind of method based on
matrix compression--adaptive cross approximation (ACA)
algorithm[5],[6] and combined with equivalent dipole-moment
technology [7],[8] to achieve the rapid filling of impedance
matrix element. In the while, the near field preconditioning
technique [9] is used to accelerate the solution of matrix
equations.
II. T
HEORY
A. Adaptive Cross Approximation algorithm
Recently, the adaptive cross approximation algorithm has
been proposed to reduce the computational complexity of
integral equation solvers. ACA is based on matrix
compression method and takes advantage of the rank-deficient
nature of the coupling matrix blocks representing
well-separated MOM interactions. The beauty of the ACA
algorithm is its purely algebraic nature and independent of
Green’s function. The ACA algorithm presented herein is
based on constructing octree model and dividing basis
functions into groups, which leads to realize the impedance
matrix decomposition into a series of different submatrices.
Among, the diagonal blocks, which correspond to self-group
interactions, as well as matrix blocks resulting from the
interactions of two touching groups, are regarded as rank-full
matrices. The off-diagonal blocks which describe remote
interactions are close to some low-rank matrices, it might be a
good idea to approximate them by low-rank matrices. Thus,
we use the ACA algorithm to carry on the effective
compression. Applying the algorithm to get the two dense
rectangular matrices
U andV , we only need to fill and store
matrix of the rows and columns.
Let the rectangular matrix
mn
Z
u
represents the coupling
between two well-separated groups in the MOM computation
domain. The ACA algorithm aims to approximate
mn
Z
u
as
mn
Z
u
with a prescribed accuracy. Particularly the ACA
algorithm constructs the approximated matrix
mn
Z
u
through a
product form, namely:
11
1
r
mn mr rn m n
ii
i
ZUV uv
uuu uu
¦
(1)
where
r
is the effective rank of the matrix
mn
Z
u
. The goal
of the ACA is to achieve:
mn mn mn mn
RZZ Z
H
uuu u
d
(2)
Where
mn
R
u
is termed the error matrix and
H
is a given
______________________________________
978-1-4673-1800-6/12/$31.00 ©2012 IEEE
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