MLFMA加速VSIE与改进MSI法：接收模式下天线-天线罩结构分析高效新策略

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本文主要探讨了在接收模式下，如何通过结合多级快速多极子算法（Multilevel Fast Multipole Algorithm, MLFMA）加速的耦合体表面积分方程（Coupled Volumesurface Integral Equation, VSIE）和改进的表面积分（Modified Surface Integration, MSI）方法，有效地分析天线-天线罩结构（Antenna-Radome Structures, ARS）。在传统的全波分析方法中，处理封闭的天线罩内的接收天线或阵列时，可能会遇到计算复杂度高、存储需求大以及高频近似方法精度受限的问题。作者提出的混合方法旨在解决这些问题，它在减少计算时间和内存需求的同时，提高了分析的准确性和有效性。 MLFMA是一种高效的电磁场求解技术，通过空间分解和局部化策略，将复杂的电磁问题分解为多个独立的子问题，从而显著降低计算复杂度。在本研究中，MLFMA被用于加速VSIE的求解过程，使得对于ARS的分析更为快速和精确。 VSIE是一种基于物理概念的数值方法，它通过将电磁场分布在物体表面来模拟电磁场的行为，适用于分析复杂的电磁散射和辐射问题。然而，标准的VSIE可能会在处理大规模结构时遇到效率问题。通过与MSI方法结合，作者对VSIE进行了优化，这种方法通过改进网格处理和边界条件处理，进一步提升了计算效率，特别是在处理AR

4884 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 9, SEPTEMBER 2014

An Efﬁcient Integral Equation/Modiﬁed Surface

Integration Method for Analysis of Antenna-Radome

Structures in Receiving Mode

Binbin Wang, Mang He, Jinbo Liu, Hongwei Chen,

Guoqiang Zhao, and Chuanfang Zhang

Abstract—An efﬁcient approach that combines the coupled volume sur-

face integral equation (VSIE) accelerated by multilevel fast multipole algo-

rithm (MLFMA) and the modiﬁed surface integration (MSI) method is pro-

posed to analyze the antenna-radome structures (ARS) in receiving mode.

The hybrid method not only reduces the computational time and memory

requirement as compared to the purely full-wave solutions, but also more

importantly overcomes the difﬁculties in conventional high-frequency ap-

proximate methods for analyzing the properties of the radome-enclosed re-

ceiving anten nas or arrays. Numerica l results are shown to illustrate the

validity, efﬁcien cy, and accuracy of the proposed method.

Index Terms—Fast algorithm, integral equation, radome, receiving a n-

tenna, surface integration.

I. INTRODUCTION

It is well known that the presence of radome has pronounced effects

on the performance of the enclosed antennas or arrays [1]. In practice

engineering, the designs of antenna and radome are usually treated as

two detached processes. A direct consequence of such situation is that

the performance of antennas may be severely degraded when working

together with a radome, even if both the antenna and radome are well

designed in the two separated procedures. Therefore, when we need to

evaluate the electromagnetic (EM) properties of the ARS, it is highly

desired that the antenna and radome can be considered as a w hole rather

than two independent parts.

A number of m ethods, including full-wave solutions [2]–[15],

high-frequency approximate methods [16]–[18], and hybrid ap-

proaches [19], [20], have been reported to deal with the ARS

problems. Among these methods, the full-wave types can evaluate

the radome effects on antennas accurately, but they are only suited to

analyze small/moderate-sized ARS since a large amount of computa-

tional time and core memory are required if the size of radome is large

in terms of wavelength, even when fast algorithms are utilized [13].

In contrast, the high-frequency methods, such as the aperture-integra-

tion surface-integration (AI-SI) [16] and physical optics (PO) [17],

[18] methods, seek approximate but efﬁcient solutions for large-size

radome with s mooth shape. The hybrid approaches, which combine

the advantages of both the full-wave and approximate methods, solve

complicated interactions between antennas and radome by using

domain-decomposition concept and choosing suitable solutions within

different domains while preserving acceptable accuracy [19], [20].

However, in almost all the above-mentioned methods, only the ef-

fects of radome on antennas’ radiation patterns have been considered,

i.e. the properties of the ARS in transmitting mode are extensively

Manuscript received F ebruary 13, 2014; revised June 27, 2014; accepted June

29, 2014. Date of publication July 02, 2014; date of current version September

01, 2014. This work was supported by the National Natural Science Foundation

of China under Grant 61471040. (Corresponding author: M. He).

B. Wang, M. He, J. Liu, G. Zhao, and C. Zhang are with the School of Infor-

mation and Electronics, Beijing Institute of Technology, Beijing 100081, China

(e-mail: hemang@bit.edu.cn).

H. Chen is with the Beijing Electro-mechanical Engineering Institu te, Beijing

100074, China.

Color versions of one or more of the ﬁgures in this communication are avail-

able online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TAP.2014.2334707

studied, while how radomes alter the performance of receiving an-

tennas is seldom taken into account. For full-wave solutions, from the-

oretical point of view, there is no difference in analyzing the A RS

working in transmitting or receiving modes although in both cases

heavy computational burdens will be faced when the electrical size of

the structure becomes large. But on the other hand, for high-frequency

approximate or hybrid methods, analyses of the ARS in two different

working situations are fundamentally distinct. In transmitting mode, ra-

diation from antennas that incidents on the i nner surface of the r

adome

is directly computed (in PO method) or by using the equivalent aper-

ture distribution (in AI-SI method), then far-ﬁeld radiation of the en-

tire structure is obtained via the equivalence theorem. Whil

eforARS

in receiving mode, which is commonly e ncountered in the telemetry,

direction ﬁnding, and passive guidance applications, the unique exci-

tation of the ARS is the incident plane wave that in th

eory can only be

generated by sources distributed on an inﬁnitely large plane. Since the

ﬁnite-sized radome cannot encompass the sources of inﬁnite extent en-

tirely, the equivalence theorem, which is the ba

sis of the PO and AI-SI

methods, cannot be used to compute the transmitted ﬁelds within the

space enclosed by radome as the excitation of the receiving antennas.

Therefore, it is difﬁcult to investigate

the properties of the ARS in re-

ceiving mode by using existing methods, especially in the analysis of

large-size structure, since in this case full-wave methods are not efﬁ-

cient whereas the use of approximate or

hybrid methods is problematic.

In this communication, an efﬁcient approach that combines the fast

algorithm accelerated VSIE solution and the MSI method is proposed

for the analysis of ARS in receiving mo

de. In Section II, a new MSI

method is devised for determination of the transmitted ﬁelds through

the radom e, and then the MLFMA accelerated VSIE solver to calcu-

late the induced currents on ant

ennasisbrieﬂy described as well. In

Section III, numerical examples are shown to demonstrate the efﬁ-

ciency and accuracy of the proposed method. Finally, conclusions are

presented in Section IV.

II. F

ORMULATION

The conﬁ guration of the A RS working in receiving mode is shown

in Fig. 1, where the radome consists of -layered dielectrics

indexed by

, , and the outermost and in-

nermost layers are free space. The thickness, volume, relative permit-

tivity, and loss tangent of the

th layer are denoted by , , ,and

, respectively. As shown in Fig. 1, the region of the radome is

with its boundary given by ,where

, ,and represent the outer, inner, and bottom surfaces of the

radome, respectively. The direction of the incident plane wave is dic-

tated by the vector

As discussed in the last section, for analysis of the receiving-mode

ARS, there are two problems to be solved: one is the calculation of the

transmitted ﬁelds

in the space enclosed by an arbitrarily-shaped

dielectric radome after the incident plane wave goes through it; and

the other one is the computation of the induced currents on receiving

antennas under the excitation ﬁelds obtained in the previous step.

A. Computation of the Transmitted Fields Within the Space Enclosed

by Radome

The conventional AI-SI method [16] is usually used for the anal-

ysis of the radome effects on radiation patterns of aperture antennas, in

which the presumed aperture distribution of the antenna is integrated to

obtain the equivalent excitation ﬁelds of the radome. However, when

we investigate the properties of the ARS in receiving mode, the SI

process in the conventional AI-SI method is not applicable, because in

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