本文選題：矩量法 + 介質(zhì)目標(biāo)�。� 參考：《西安電子科技大學(xué)》2016年博士論文

【摘要】：雷達(dá)在第二次世界大戰(zhàn)中得到了迅速的發(fā)展,時(shí)至今日發(fā)展成為能夠代表一個(gè)國家軍事工業(yè)先進(jìn)水平的典型案例。雷達(dá)系統(tǒng)的設(shè)計(jì)和目標(biāo)電磁散射特性的預(yù)估與系統(tǒng)前端天線輻射特性的分析是緊密相關(guān)的。目標(biāo)電磁散射特性的預(yù)估是以電磁計(jì)算方法為基礎(chǔ)的,其最終要求則是能夠?qū)ν庑螐?fù)雜和電大尺寸的目標(biāo)進(jìn)行精確且快速的分析。另一方面,天線輻射特性分析的難點(diǎn)之一在于能夠有效計(jì)算各種復(fù)雜載體平臺(tái)對(duì)天線性能的影響。本文基于以上背景并結(jié)合國防預(yù)研項(xiàng)目,著重研究了電磁算法中有關(guān)介質(zhì)目標(biāo)的矩量法及其快速算法,并結(jié)合掃頻算法實(shí)現(xiàn)了針對(duì)介質(zhì)目標(biāo)的快速寬帶散射分析。此外,對(duì)載體平臺(tái)上天線輻射特性的快速分析進(jìn)行了相關(guān)研究。本文的主要工作可以概括為以下六個(gè)方面：1.詳細(xì)研究了電場(chǎng)積分方程的矩量法。介紹了矩量法的數(shù)學(xué)原理,根據(jù)理想導(dǎo)體邊界條件建立了電場(chǎng)積分方程。著重討論了RWG基函數(shù)的特點(diǎn)、伽略金檢驗(yàn)過程和高斯數(shù)值積分,對(duì)奇異性問題進(jìn)行了細(xì)致的公式推導(dǎo)。2.詳細(xì)研究了基于PMCHWT方程和體積分方程的矩量法。從均勻介質(zhì)目標(biāo)散射模型的等效外問題和等效內(nèi)問題出發(fā),闡述了PMCHWT方程的形成過程。用矩量法對(duì)PCMHWT方程進(jìn)行求解,并討論了子阻抗矩陣的對(duì)稱性和其奇異性問題。介紹了基于四面體剖分的SWG基函數(shù)及其的特點(diǎn)。用矩量法對(duì)適用于一般介質(zhì)目標(biāo)的體積分方程進(jìn)行求解,并對(duì)奇異性問題給出了詳細(xì)的公式推導(dǎo)。對(duì)介質(zhì)金屬混合目標(biāo)的矩量法進(jìn)行了拓展研究。3.介紹了積分方程-快速傅里葉變換方法(IE-FFT)中均勻笛卡爾網(wǎng)格的建立和自由空間格林函數(shù)的拉格朗日多項(xiàng)式插值技術(shù),形象地展示了離散格林函數(shù)矩陣的三重Toeplitz特性,完整的闡述了具有三重Toeplitz特性的矩陣和向量乘積的快速傅里葉變換(FFT)加速原理。針對(duì)矩量法內(nèi)存需求大和求解矩陣方程計(jì)算復(fù)雜度較高的問題,研究了基于PMCHWT方程的IE-FFT技術(shù),并比較了兩種可能的FFT加速策略,將內(nèi)存和計(jì)算復(fù)雜度降低到O(N1.5)和O(N1.5log N)。同樣,研究了基于體積分方程的IE-FFT方法,有效的將內(nèi)存和計(jì)算復(fù)雜度降低到O(N)和O(N log N)。4.提出將體積分方程矩量法分別結(jié)合漸近波形估計(jì)和最佳一致有理逼近來快速預(yù)估一般介質(zhì)目標(biāo)的寬帶電磁散射特性。第一種方法在給定頻點(diǎn)對(duì)矩陣方程中的阻抗矩陣、激勵(lì)向量和未知向量進(jìn)行泰勒展開,對(duì)關(guān)于頻率的多項(xiàng)式進(jìn)行合并同類項(xiàng)來求解未知向量的泰勒展開系數(shù),通過Pad6逼近對(duì)未知向量做進(jìn)一步展開來延展帶寬。第二種方法在給定的整個(gè)帶寬內(nèi)選定切比雪夫節(jié)點(diǎn),計(jì)算其對(duì)應(yīng)波數(shù)上的等效體電流密度,并通過梅利逼近來提高計(jì)算精度。將PMCHWT-IE-FFT和最佳一致有理逼近相結(jié)合來快速分析均勻介質(zhì)目標(biāo)的寬帶散射特性,通過FFT加速技術(shù)縮短了最佳一致有理逼近方法中電磁流密度的求解時(shí)間。5.針對(duì)矩量法物理光學(xué)混合算法(MoM-PO)中修正阻抗矩陣填充計(jì)算復(fù)雜度較大的問題,提出將MoM-PO和IE-FFT相結(jié)合的IE-FFT-PO方法。首先對(duì)修正阻抗矩陣進(jìn)行矩陣分解得到矩量法區(qū)和物理光學(xué)區(qū)之間互阻抗矩陣和耦合矩陣的乘積。稀疏存儲(chǔ)自阻抗矩陣、互阻抗矩陣和耦合矩陣的阻抗元素,并對(duì)矩陣方程求解每一步迭代中的三次矩陣向量積運(yùn)算進(jìn)行FFT加速。6.針對(duì)載體平臺(tái)上多天線的輻射問題,提出基于MoM-PO方法的分區(qū)技術(shù),將每一個(gè)天線及其附近區(qū)域劃分為一個(gè)矩量法區(qū),剩余部分為物理光學(xué)區(qū)。該方法在考慮每一個(gè)矩量法區(qū)和物理光學(xué)區(qū)之間耦合作用的基礎(chǔ)上,進(jìn)一步考慮多個(gè)矩量法區(qū)之間的相互作用。相比傳統(tǒng)MoM-PO方法,其結(jié)果是修正阻抗元素個(gè)數(shù)的大幅減少,從而縮短自阻抗矩陣需要的修正時(shí)間。借鑒迭代MoM-PO的思想,提出了分區(qū)迭代的MoM-PO方法,相比分區(qū)MoM-PO方法,進(jìn)一步縮短了載體平臺(tái)多線天線輻射問題分析所需要的時(shí)間。
[Abstract]:Radar has developed rapidly in the Second World War, and today it has developed into a typical case that can represent the advanced level of a country's military industry. The design of the radar system and the prediction of the target electromagnetic scattering characteristics are closely related to the analysis of the radiation characteristics of the front end of the system. The prediction of the target electromagnetic scattering characteristics It is based on the electromagnetic calculation method, and its final requirement is to be able to accurately and quickly analyze the complex and large size targets. On the other hand, one of the difficulties of antenna radiation analysis is to effectively calculate the influence of various complex carrier platforms on the performance of the antenna. This paper is based on the background and the national defense. In the pre research project, the moment method and its fast algorithm about the medium target in the electromagnetic algorithm are emphatically studied, and the fast broadband scattering analysis for medium targets is realized with the sweep frequency algorithm. In addition, the rapid analysis of the antenna radiation characteristics on the carrier platform is studied. The main work of this paper can be summarized as the following six parties Surface: 1. the method of moment of the electric field integral equation is studied in detail. The mathematical principle of the moment method is introduced. The integral equation of the electric field is established according to the ideal conductor boundary condition. The characteristics of the RWG basis function, the Galerkin test process and the Gauss numerical integration are emphatically discussed. The detailed formula derivation of the singularity problem is carried out in the.2. detailed study based on the P The method of moment of the MCHWT equation and the body integral equation. Based on the equivalent external problem and the equivalent internal problem of the uniform medium target scattering model, the formation process of the PMCHWT equation is expounded. The PCMHWT equation is solved by the moment method, and the symmetry and singularity of the sub impedance matrix are discussed. The SWG base function based on the tetrahedral partition is introduced. The method of moment method is used to solve the volume equation applicable to the general medium target, and the detailed formula derivation is given to the singularity problem. The expansion of the moment method for the medium metal mixed target is extended..3. introduces the establishment of the uniform Cartesian grid in the integral equation fast Fourier transform square method (IE-FFT). The Lagrange polynomial interpolation technique of the free space Green function shows the three Toeplitz properties of the discrete Green function matrix, and expounds the fast Fu Liye transform (FFT) acceleration principle of the matrix and the vector product of the three heavy Toeplitz properties. The problem of high complexity is to study the IE-FFT technology based on PMCHWT equation, and compare two possible FFT acceleration strategies to reduce the memory and computational complexity to O (N1.5) and O (N1.5log N). Also, the IE-FFT method based on the body integral equation is studied. The memory and computational complexity are effectively reduced to O (N) and O (O). The method of moment of the body integral equation combines the Asymptotic Waveform Estimation and the best uniform rational approximation to quickly estimate the wide-band electromagnetic scattering characteristics of the general medium target. The first method is carried out by Taylor expansion of the impedance matrix, the excitation vector and the unknown vector in the matrix equation at a given frequency point, and the polynomial of the frequency is merged with the same kind. The Taylor expansion coefficient of the unknown vector is solved by the term, and the unknown vector is further expanded to extend the bandwidth by Pad6 approximation. The second methods select the Chebyshev node in the given whole bandwidth, calculate the equivalent body current density on the corresponding wave number, and improve the calculation precision by Melly approximation. Combining rational approximation to fast analysis the wide-band scattering characteristics of uniform medium targets, the time.5. for solving the electromagnetic flow density in the best uniform rational approximation method is shortened by FFT acceleration technology. The problem of calculating the complexity of the modified impedance matrix in the moment method physical optical mixing algorithm (MoM-PO) is solved, and MoM-PO and I are proposed. The IE-FFT-PO method combined with E-FFT. First, the matrix decomposition of the modified impedance matrix is used to obtain the product of the mutual impedance matrix and the coupling matrix between the moment method region and the physical optical region. The impedance matrix of the self impedance matrix, the mutual impedance matrix and the coupling matrix are sparsely stored, and the matrix formula is used to solve the three matrix vectors in each iteration of the matrix. The product operation is carried out by FFT acceleration.6. to solve the radiation problem of multi antenna on the carrier platform. The partition technique based on the MoM-PO method is proposed. Each antenna and its nearby region are divided into a moment method region, and the remaining part is the physical optical region. In one step, the interaction between the multiple moment method regions is considered. Compared with the traditional MoM-PO method, the result is a significant reduction in the number of impedance elements, thus shortening the correction time needed for the self impedance matrix. Using the idea of iterative MoM-PO, a MoM-PO method of partition iteration is proposed. The phase is compared to the partition MoM-PO method, and the carrier platform is further shortened. The time needed for the analysis of the radiation problem of a multiwire antenna.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN011

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