Fast and accurate analysis of broadband RCS
using method of moments with loop-tree
basis functions
ISSN 1751-8725
Received on 21st March 2014
Accepted on 19th November 2014
doi: 10.1049/iet-map.2014.0189
www.ietdl.org
Hai-Lin Dong, Shu-Xi Gong
✉
, Peng-Fei Zhang, Ji Ma, Bo Zhao
National Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi’an, Shaanxi 710071, People’s Republic of China
✉ E-mail: shxgong@xidian.edu.cn
Abstract: An efficient method for w ide-band electrom agnetic (EM) scattering properties analysis of thre e-dimensi onal
arbitrarily shaped perfectly electric conductor (PEC) objects is proposed in this study. The electric field integral
equation (EFIE) is solved by the method of moments (MoM) base on the loop-tree basis functions. The EM properties
not only can be achieved accurately in high frequency band, but also in low frequency band within the de sired
bandwidth using loop-tree basis functions. To improve the computation efficiency, the Maehly approximation method
is utilised. Compared with the direct solution method and asymptotic waveform evaluation technique , the proposed
technique is found to be efficient in a broadband and wide ang ular domain with the low er central processing un it time
required and without loss of accuracy.
1 Introduction
Analysing the electromagnetic (EM) scattering of an arbitrary shaped
perfectly electric conductor (PEC) accurately over a wide frequency
band or a broad angular domain is very important for the research of
radar stealth, imaging technology and target identification. In
modern EM computation field, the solution of surface integral
equation using method of moments (MoM) has been a very useful
tool to accurately predict radar cross section (RCS) of arbitrarily
shaped PEC objects in frequency domain [1–3].
However, for the traditional MoM, the low frequency breakdown
problem limits its application in EM problem analysis when the low
frequency band is considered. Some papers have investigated the low
frequency limit problems by many numerical examples [4, 5]. After
the previous researchers’ work, this problem can be avoided by
quasi-Helmholtz decompositions or Calderón preconditioning
techniques [6, 7]. The decomposition can be achieved by the
loop-tree method [6]. Thus the EM properties analysis limit
problem in low frequency can be overcome by introducing the
loop-tree basis function. These bases separate the contributions
from magnetic vector potential and electric scalar potential.
Therefore the contribution from the vector potential will not be
swamped by that from the scalar potential and the current
distribution on PEC can be got accurately [8]. To expand the
application scopes of loop-tree decompositions method for
analysing EM properties, there are some efforts ongoing in this
field. The conditioning of loop-tree and loop-star Gram matrices is
analysed, exploring their spectral properties theoretically and
numerically in [9 ]. In [10], a Helmholtz-stable fast solution for
electric field integral equation (EFIE) is proposed, which reduces
the matrix-vector multiplication cost by using the effectiveness of
quasi-Helmholtz decompositions or Calderón preconditioning
techniques to solve the ‘charge cancellation’ problem in low
frequency. A fast solver for very dense meshes and multi-scale
problems is presented to solve the realistic problems in the low
frequency region [11]. The loop-star and loop-tree basis function
approach is applied to analyse the complicated and mixed
geometries, including open or close surfaces, surface-wire
junctions and printed structures, which expands the range of
application of these bases for realistic problems [12]. In [13], the
method of Green’s function interpolation with fast Fourier
transform (FFT) fast solver is utilised to analyse the large
multi-scale wire-surface structures, and the solution is expanded to
low frequency with the help of solenoidal and non-solenoidal
decomposition of the unknown current.
Another problem has to do with its numerical solution time in
broadband and wide angle domain EM properties solving. For the
RCS computation using the MoM, the MoM is still
time-consuming since each frequency point or angle requires a
repeated solution of the induced currents. For years there is a
strong desire to find efficient techniques that can efficiently
simulate the response over a broadband and wide angle domain to
predict RCS of the targets. If the response over a wide band is of
interest, one has to repeat the calculations at each frequency point,
which requires much more time. To over this dif ficulty, some
techniques such as asymptotic waveform evaluation (AWE)
technique [14–16] and model-based parameter estimation [
17],
have been developed to decrease the computation burden.
In the AWE technique, the induced current is expanded in the
Taylor series around a frequency or an angle, and the rational
function approach is used to improve the accuracy. As compared
with using MoM at each frequency point or incident angle, the
AWE method is found to be superior in terms of the central
processing unit (CPU) time to predict RCS. The AWE technique
was originally developed for high-speed circuit analysis [18] and
then was applied to solving scattering problem. In [19], the
method of AWE technique combined with the FFT has also been
applied to fast RCS computation. The AWE incorporated finite
element/boundary integral (FE/BI) method was presented in [20].
Nevertheless, in AWE technique, most CPU time is spent on the
generation of the impedance matrix and its derivatives, and the
accuracy of the Taylor series is limited by the radius of
convergence. Recently, Maehly approximation [21] has been also
applied to the fast frequency sweep analysis successfully.
Compared with the AWE technique, the major advantage of the
Maehly approximation is that it does not require the complex high
order derivatives of impedance and excitation matrix. For desired
frequency or incident angular domains, the frequency points or
incident angle points corresponding to the Chebyshev nodes are
found by transformation of coordinates and the induced current is
represented by the Chebyshev series [22]. The coefficients of
Chebyshev series are then matched via the Maehly approximation to
a rational function in order to improve the accuracy of the numerical
solution. The rational function obtained can be used as the best
uniform rational approximation [23, 24].Thereisnoneedtostore
and solve the high derivatives of impedance and excitation matrix.
IET Microwaves, Antennas & Propagation
Research Article
IET Microw. Antennas Propag., 2015, Vol. 9, Iss. 8, pp. 775–780
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