本文選題：電磁散射　切入點(diǎn)：矩量法　出處：《南京郵電大學(xué)》2015年博士論文

【摘要】：采用數(shù)值方法可以靈活地對(duì)任意目標(biāo)建模仿真求解,己成為獲得目標(biāo)散射特征的重要方法,是計(jì)算電磁學(xué)的重要研究領(lǐng)域。在各種數(shù)值方法中,矩量法由精度高,未知量規(guī)模小而得到了廣泛應(yīng)用,但是求解矩量法得到的線性方程組需要大量的存儲(chǔ)空間和計(jì)算時(shí)間。為了克服上述問題發(fā)展出了一系列快速方法,其中遠(yuǎn)區(qū)作用矩陣塊的高效表示是構(gòu)建快速算法的重點(diǎn)和難點(diǎn)。退化核技術(shù)可以有效用于矩陣的低秩近似表示。本文以層次型矩陣(H矩陣)框架為基礎(chǔ),深入研究了格林函數(shù)的快速退化核構(gòu)造方法,用來構(gòu)建快速算法求解電磁散射問題。主要研究內(nèi)容和貢獻(xiàn)主要分為以下幾個(gè)方面：1.提出一種線性計(jì)算復(fù)雜度的公共邊生成方法,用于采用RWG基函數(shù)矩量法通用求解方法的前處理中。該算法基本思路為只通過比較鄰近三角形面元的頂點(diǎn)編號(hào)來得到公共邊信息,從而將計(jì)算復(fù)雜度由O(N2)減少為O(N),這里N為三角形面元數(shù)目。該算法可以集成到通用的仿真軟件和算法測試平臺(tái)中。此外,該算法己成功推廣應(yīng)用于快速生成四面體體元剖分的公共面。2.研究了采用Lagrange多項(xiàng)式和徑向基函數(shù)(RBF)構(gòu)造的插值退化核。格林函數(shù)為個(gè)震蕩函數(shù),基于距離的徑向基函數(shù)插值的效率更高,只需要更少的插值點(diǎn)就能得到較高的插值精度。針對(duì)導(dǎo)體散射問題,提出一種近表面插值網(wǎng)格來減少插值點(diǎn)的數(shù)目。相比傳統(tǒng)的均勻插值網(wǎng)格,近表面插值網(wǎng)格只選用靠近目標(biāo)體表面的點(diǎn),從而可以將插值插值點(diǎn)的數(shù)目由O(k3)下降為O(k2),其中k為每一維上的插值點(diǎn)數(shù)目。計(jì)算效率大幅提高,同時(shí)保持精度基本不變。3.基于分層基層次型矩陣(H2矩陣)框架,提出了一種用于求解導(dǎo)體電磁散射問題的混合插值網(wǎng)格的快速算法。該方法采用高斯徑向基函數(shù)構(gòu)造插值退化核函數(shù),根據(jù)不同層劃分得到的立方體塊大�。簩�(duì)于較小的塊,插值網(wǎng)格選用均勻網(wǎng)格,其它塊選用近表面插值網(wǎng)格。該方法結(jié)合了兩種網(wǎng)格的優(yōu)點(diǎn)。相比于只采用均勻網(wǎng)格的方法,所提方法的計(jì)算量和存儲(chǔ)量都有所下降。4.提出了一種新穎的指數(shù)退化核函數(shù)。指數(shù)退化核函數(shù)可以將格林函數(shù)源點(diǎn)與場點(diǎn)作用分離,得到的轉(zhuǎn)移矩陣是對(duì)角矩陣,相比于多極子展開,達(dá)到相同精度時(shí)所需展開項(xiàng)數(shù)減少。從而可以有效地加快迭代求解算法中的矩陣向量乘法運(yùn)算。在此基礎(chǔ)上,提出一種新的方向選擇方案,可以進(jìn)一步減少展開項(xiàng)數(shù)至多極子展開的一半,且隨著塊尺寸變大比多極子展開增長更慢。數(shù)值算例驗(yàn)證了算法的有效性。
[Abstract]:Using the numerical method can flexibly to arbitrary target modeling simulation, has become an important method to obtain the target scattering characteristics, is an important research field of computational electromagnetics. In a variety of numerical methods, the method of moments by the high precision, the unknown quantity of small scale and has been widely used, but for the moment method of linear equations need a lot of computing time and memory space. In order to overcome the problems of the development of a series of rapid method, the far zone matrix block, that is important and difficult to construct a fast algorithm. The degradation of nuclear technology can be effectively used for the low rank matrix approximation. Based on the hierarchical matrix (H matrix) framework the rapid degradation of nuclear construction methods, in-depth study of the Green function, used to construct a fast algorithm for solving electromagnetic scattering problems. The main research contents and contributions are mainly divided into the following several aspects 1.: This paper proposes a linear computational complexity common edge generation method, used for pretreatment with RWG basis function moment method. The general method for solving the basic idea of the algorithm is to get the public information through the number of points is only edge adjacent triangle element, thus the computational complexity from O (N2) to reduce O (N), where N is the number of triangle element. This algorithm can be integrated into the simulation software and the algorithm of common test platform. In addition, the public face.2. the algorithm has been successfully applied to the rapid generation of tetrahedral element subdivision was studied by Lagrange polynomial and radial basis function (RBF) structure the interpolation degenerated kernel. The Green function as a shock function, efficiency based on radial basis function interpolation distance higher, requiring fewer interpolation points can get higher accuracy. According to the scattering problem, proposes a near surface interpolation grid To reduce the number of interpolation points. Compared with the traditional uniform grid interpolation, near surface interpolation grid use only near the target surface, which can be the number of interpolation points by O (K3) O (K2), decreased the K for the purpose of interpolation points for each dimension. At the same time, a substantial increase in the efficiency of calculation. Keep the accuracy invariable.3. layered base matrix (H2 matrix) based on the framework, put forward a fast algorithm for solving electromagnetic scattering problems of conductor mixed interpolation grid. This method adopts Gauss radial basis function interpolation degenerate kernel, according to cube block size in different layers were divided: for smaller blocks, interpolation the grid used the uniform grid, other blocks are made of near surface interpolation grid. This method combines the advantages of the two kinds of grid. Compared to the method using only uniform grid, the amount of calculation and storage of the proposed method are decreased .4. proposes a novel index index. Degenerate kernel degenerate kernel can separate the source points and field Green function, the transfer matrix is a diagonal matrix, compared to the multipole expansion, the expansion terms reduce to achieve the same precision. It can effectively accelerate the matrix vector multiplication in iterative algorithm. On this basis, put forward a new direction selection scheme can be further reduced by half approximation to multipole expansion, and the block size becomes larger than multipole expansion slower growth. Numerical examples show the validity of the algorithm.

【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN011

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