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首页自适应频采样改进Stoer-Bulirsch算法:宽带等效源重构及其精度提升
自适应频采样改进Stoer-Bulirsch算法:宽带等效源重构及其精度提升
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本文档探讨了在无线通信领域的研究工作中,如何通过自适应频率采样技术来改进Stoer-Bulirsch算法在宽带等效源重构方法中的应用。该研究关注于天线和传播领域的高级计算,具体是在设计和分析复杂的电磁场结构时,如何构建等效电路模型,以便更精确地模拟实际场景中的辐射行为。 Stoer-Bulirsch算法是一种数值积分算法,用于求解微分方程中的积分问题,常用于解决多体动力学中的数值稳定性问题。在本研究中,它被巧妙地结合了自适应频率采样策略,这允许算法在处理宽频带信号时更加高效,尤其是在处理宽带天线或波导系统时,这些系统的特性随频率变化显著。 关键的技术难点在于,为了生成等效的电磁源,即等效电荷和磁矩,需要将实际的离散电场和磁场成分转换为具有特定材料属性(如电导率和磁导率)的等效球体。这些等效球体的电偶极矩反映了它们对周围电磁场的响应,而这些响应又受到自身电偶极矩之间耦合的影响。作者采用了一种近似分析的方法,即基于有限差分时间域(FDTD)的准解析CDA(Circuit-Differential Approach),这种方法将DGF(差分格林函数)项替换为数值计算的FDTD兼容版本,以准确考虑这种耦合效应。 结果显示,等效球体之间的耦合程度不容忽视,这对每个球体的极化状态产生了显著影响。通过数值预测子单元模型的低频散射特性,研究者能够验证理论预期的性能,并进一步优化天线的设计和性能参数。 文献引用部分列举了先前关于天线理论和电磁场计算的研究,这些工作为本文提供了基础理论和技术支持。这项研究不仅提升了计算效率,还对提高宽带无线通信系统的设计和仿真精度有着重要的实际应用价值。
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5338 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 10, OCTOBER 2013
that can be defined along the immediately surrounding discrete elec-
tric and magnetic field components. In order to create these equivalent
dipole moments, appropriate material properties need to be assigned
across the corresponding field components. Consequently, the equiva-
lent dipole moments become the moments of either dielectric or mag-
netic spheres.
It was further demonstrated that the accurate computation of these
properties requires to take into account the coupling between the dipole
moments of the aforementioned equivalent spheres. This is achieve
d
by utilizing a quasi-analytical version of the CDA, that is a CDA ap-
proach where the involved DGF terms are substituted by their numer-
ically computed, FDTD compatible, ones. It turns out that the le
vel
of coupling is by no means negligible, and it considerably affects the
polarization of each equivalent sphere. The low frequency scattering
characteristics of the subcell model were numericall
y predicted, and
the theoretically expected behavior was verified.
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A Wide-Band Equivalent Source Reconstruction
Method Exploiting the Stoer-Bulirsch Algorithm
With the Adaptive Frequency Sampling
Ping Li, Yan Li, Li Jun Jiang, and Jun Hu
Abstract—Conventional equivalent source reconstruction methods
are only operating at a single frequency point each time. However, for
wide-band radiators, their computation cost of the source reconstruction
increases with the number of frequency points. In this communication, a
wide-band equi valent source reconstruction method (WB-SRM) based on
the Neville-type Stoer-Bulirsch (SB) algorithm is develo ped. Since the SB
algorithm is a recursive tabular method, it can perform the interpolation
over a broadband using a single rational function without any singularity
issue. Supported by the adaptive frequency sampling (AFS) scheme, the
number of required sampling data is significantly reduced, wh ich leads to
much better computational efficiency. Dur ing the AFS process, three fitting
models (FM) are considered: two are “triangle rules,” and another one
is “rhombus rule.” In this communication, a bisection searching strategy
is performed. Furthermore, to achieve high-order a ccuracy, the Nyström
method is implemented. Numerical examples are presented to validate the
proposed WB-SRM and demonstrate its accuracy and applications.
Index Terms—Adaptive frequency sampling, electric field integral equa-
tion, fitting m o dels, Nyström met hod, Stoer-Bulirsch (SB) algorithm , wide-
band source reconstruction.
I. INTRODUCTION
Inverse equivalent source reconstruction methods are a broadly em-
ployed near-field (NF) measu remen
t post-processing technique. With
this equivalent source, hot spot identification, source error detection,
near-field to near/far-field transformation, etc., can be conveniently
performed. Moreover, source
reconstruction is more flexible in han-
dling complex geometries where equivalent current source as well as
the measurement domain reside. These m erits are hard to be observed
in the wave expansion method
s [1]–[3].
The source reconstruction method (SRM) has received intensive
attention for near-field far-field (NF-FF) transformations. R ese archers
firstly facilitate SRM by pl
acing equivalent electric or magnetic
current sources at an infinite large planar perfect electric conductor
Manuscript received D ecem ber 27, 2012; revised June 05, 2013; accepted
July 06, 2013. Date of publication July 18, 2013; date of current version October
02, 2013. T his work was supported in part by the Research Grants Council of
Hong K ong (GRF 713011 and G RF 712612), US AOA RD (NSFC 61271158),
and US A OARD FA2386-12-1-4082.
P. Li and L. J. Jiang are with the Department of Ele ctrica l and Electronic Engi-
neering, the University of Hong Kong, Hong Kong, China (e-mail: liping@eee.
hku.hk; jianglj@hku.hk).
Y. Li a nd J. Hu are with the Depar tment of Microwave E ngineeri ng, Univer-
sity of Electronic Science and Technology of China, Cheng Du, China.
Color versions of one or more of the figures in th is communica tion are avail-
able online at http://ieeexplore.ieee.org.
Digital Object Identifier 1
0.1109/TAP.2013.2274032
0018-926X © 2013 IEEE
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