预修正快速傅立叶变换方法在电磁散射分析中的研究及应用
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摘要
在雷达探测、目标识别、隐身和反隐身等技术领域中,快速分析目标的电磁散射特性具有重要意义。随着越来越多的复合材料被用于各种目标和设备,对任意金属和多种介质构成的复杂目标进行快速准确的散射分析已经成为热门研究课题。本文以电磁积分方程为理论基础,以矩量法为求解方法,使用预修正快速傅立叶变换(P-FFT)方法来加速求解过程。主要致力于对P-FFT方法的关键问题开展研究,对算法进行改进,并将其应用于快速分析复杂目标的电磁散射特性。
本文可以分为三个部分。第一部分主要研究利用矩量法求解电磁积分方程的基本理论和具体方法;第二部分主要根据P-FFT方法的原理和实现方法,利用P-FFT方法分析金属目标、介质目标、金属-介质混合目标;第三部分主要针对P-FFT方法的固有缺陷,提出并实现多层P-FFT方法,并将其性能与P-FFT方法进行比较。
在第一部分中,首先从基本电磁理论出发推导出电磁积分方程,然后介绍矩量法求解积分方程的基本思想和一般步骤,随后构建应用于金属目标的RWG基函数、应用于介质目标的SWG基函数,最后详细说明了利用RWG基函数离散金属目标的面积分方程、利用SWG基函数离散介质目标的体积分方程、利用RWG基函数和SWG基函数离散金属-介质混合目标的体-面结合积分方程的具体方法以及所得到的线性方程组。
在第二部分中,首先阐述P-FFT方法的基本思想、一般步骤、理论依据以及各个算子的具体实现方法,然后提出模板拓扑的改进方法,实现一种新的模板拓扑,以达到降低近区预修正存储需求的目的,最后分别将P-FFT方法应用于分析金属目标、非均匀介质目标以及金属-介质混合目标的RCS,并分别考察P-FFT方法的计算精度、存储需求和计算复杂度。
在第三部分中,针对P-FFT方法分析金属目标、空心介质目标和金属-介质混合目标时效率较低的问题,提出多层P-FFT方法,构造适用于多层P-FFT方法的模板拓扑和多层模板结构,然后实现多层P-FFT方法的层间投影、插值、预修正等算子,考察多层P-FFT方法分析各类目标时的计算精度、存储需求和计算复杂度,最后将多层P-FFT方法应用于分析各类目标的RCS,并比较多层P-FFT方法与P-FFT方法各自的适用范围。
The fast analysis of electromagnetic scattering characteristic of targets plays an important role in the technical areas of radar detection, radar target identification and radar cloaking and anti-cloaking. It has been a hot research topic to analyze the electromagnetic scattering from complex targets that compose of arbitrary metal and dielectric, partly because more and more composite materials are used in more and more targets and equipments. Aiming at these backgrounds, with the electromagnetic field integral equations being used as theoretical basis and the method of moments being used as solving technique the precorrected-FFT method is employed to accelerate the solving process in this thesis. The primary research focuses on studying some key problems of the precorrected-FFT method, improving the method, and applying the method to the fast analysis of EM scattering characteristics of complex targets.
This thesis is made up of three parts. The first part of this thesis focuses on studying the basic theory and the specific implementation to solve electromagnetic field integral equations with method of moments. The second part focuses on applying the precorrected-FFT method to analyze metallic objects, dielectric objects, and composite metallic-dielectric objects based on its principle and implementation. In the third part, the multilevel precorrected-FFT method is presented and implemented to overcome the intrinsic drawback of the precorrected-FFT method, and then the performances of both methods are compared.
In the first part of this thesis, the electromagnetic field integral equations are deduced from the basic electromagnetic theory firstly. Then the basic ideas and the general process of solving the integral equation with method of moments are introduced. And then the RWG basis function for metallic objects and SWG basis function for dielectric objects are constructed. Finally, the specific processes of the discretization of the surface integral equation of metallic objects with RWG basis function, the discretization of the volume integral equation of dielectric objects with SWG basis function, and the discretization of the volume-surface integral equation of composite metallic-dielectric objects with RWG and SWG basis functions are explained in detail, as well as the resulting linear equations.
In the second part of this thesis, the basis ideas, the general process, the theory foundation and the implementation of the operators of the precorrected-FFT method are set forth firstly. Then a new stencil topology is implemented to reduce the memory requirement of near-zone precorrections. Finally, the precorrected-FFT method is applied to analyze the RCSs of metallic objects, dielectric objects and composite metallic-dielectric objects, with its accuracy, memory requirement and computation complexity being investigated.
In the last part of this thesis, the multilevel precorrected-FFT method is presented to overcome the poor efficiency of the precorrected-FFT method when analyzing metallic objects, hollow dielectric objects and composite metallic-dielectric objects. Then an improved stencil topology and the multilevel stencil structure adapted to the multilevel precorrected-FFT method are constructed. And then the inter-level operators such as projection, interpolation and precorrection are implemented. And then the accuracy, memory requirement and computation complexity of the multilevel precorrected-FFT method are investigated in combination with the analysis of various objects. Finally, the multilevel precorrected-FFT method is applied to analysis the RCSs of various objects, followed by the range of application of the multilevel precorrected-FFT method and the range of application of the precorrected-FFT method being compared.
本文可以分为三个部分。第一部分主要研究利用矩量法求解电磁积分方程的基本理论和具体方法;第二部分主要根据P-FFT方法的原理和实现方法,利用P-FFT方法分析金属目标、介质目标、金属-介质混合目标;第三部分主要针对P-FFT方法的固有缺陷,提出并实现多层P-FFT方法,并将其性能与P-FFT方法进行比较。
在第一部分中,首先从基本电磁理论出发推导出电磁积分方程,然后介绍矩量法求解积分方程的基本思想和一般步骤,随后构建应用于金属目标的RWG基函数、应用于介质目标的SWG基函数,最后详细说明了利用RWG基函数离散金属目标的面积分方程、利用SWG基函数离散介质目标的体积分方程、利用RWG基函数和SWG基函数离散金属-介质混合目标的体-面结合积分方程的具体方法以及所得到的线性方程组。
在第二部分中,首先阐述P-FFT方法的基本思想、一般步骤、理论依据以及各个算子的具体实现方法,然后提出模板拓扑的改进方法,实现一种新的模板拓扑,以达到降低近区预修正存储需求的目的,最后分别将P-FFT方法应用于分析金属目标、非均匀介质目标以及金属-介质混合目标的RCS,并分别考察P-FFT方法的计算精度、存储需求和计算复杂度。
在第三部分中,针对P-FFT方法分析金属目标、空心介质目标和金属-介质混合目标时效率较低的问题,提出多层P-FFT方法,构造适用于多层P-FFT方法的模板拓扑和多层模板结构,然后实现多层P-FFT方法的层间投影、插值、预修正等算子,考察多层P-FFT方法分析各类目标时的计算精度、存储需求和计算复杂度,最后将多层P-FFT方法应用于分析各类目标的RCS,并比较多层P-FFT方法与P-FFT方法各自的适用范围。
The fast analysis of electromagnetic scattering characteristic of targets plays an important role in the technical areas of radar detection, radar target identification and radar cloaking and anti-cloaking. It has been a hot research topic to analyze the electromagnetic scattering from complex targets that compose of arbitrary metal and dielectric, partly because more and more composite materials are used in more and more targets and equipments. Aiming at these backgrounds, with the electromagnetic field integral equations being used as theoretical basis and the method of moments being used as solving technique the precorrected-FFT method is employed to accelerate the solving process in this thesis. The primary research focuses on studying some key problems of the precorrected-FFT method, improving the method, and applying the method to the fast analysis of EM scattering characteristics of complex targets.
This thesis is made up of three parts. The first part of this thesis focuses on studying the basic theory and the specific implementation to solve electromagnetic field integral equations with method of moments. The second part focuses on applying the precorrected-FFT method to analyze metallic objects, dielectric objects, and composite metallic-dielectric objects based on its principle and implementation. In the third part, the multilevel precorrected-FFT method is presented and implemented to overcome the intrinsic drawback of the precorrected-FFT method, and then the performances of both methods are compared.
In the first part of this thesis, the electromagnetic field integral equations are deduced from the basic electromagnetic theory firstly. Then the basic ideas and the general process of solving the integral equation with method of moments are introduced. And then the RWG basis function for metallic objects and SWG basis function for dielectric objects are constructed. Finally, the specific processes of the discretization of the surface integral equation of metallic objects with RWG basis function, the discretization of the volume integral equation of dielectric objects with SWG basis function, and the discretization of the volume-surface integral equation of composite metallic-dielectric objects with RWG and SWG basis functions are explained in detail, as well as the resulting linear equations.
In the second part of this thesis, the basis ideas, the general process, the theory foundation and the implementation of the operators of the precorrected-FFT method are set forth firstly. Then a new stencil topology is implemented to reduce the memory requirement of near-zone precorrections. Finally, the precorrected-FFT method is applied to analyze the RCSs of metallic objects, dielectric objects and composite metallic-dielectric objects, with its accuracy, memory requirement and computation complexity being investigated.
In the last part of this thesis, the multilevel precorrected-FFT method is presented to overcome the poor efficiency of the precorrected-FFT method when analyzing metallic objects, hollow dielectric objects and composite metallic-dielectric objects. Then an improved stencil topology and the multilevel stencil structure adapted to the multilevel precorrected-FFT method are constructed. And then the inter-level operators such as projection, interpolation and precorrection are implemented. And then the accuracy, memory requirement and computation complexity of the multilevel precorrected-FFT method are investigated in combination with the analysis of various objects. Finally, the multilevel precorrected-FFT method is applied to analysis the RCSs of various objects, followed by the range of application of the multilevel precorrected-FFT method and the range of application of the precorrected-FFT method being compared.
引文
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