本文關(guān)鍵詞： 高階矩量法 高階基函數(shù) 棱邊基函數(shù) 面元基函數(shù) 修正勒讓德多項(xiàng)式高階基函數(shù) 高階曲面建模　出處：《南京郵電大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：RWG基函數(shù)定義在具有公共棱邊的三角形對上,建立在RWG基函數(shù)上的矩量法要求剖分的每個(gè)三角形的邊長在十分之一波長左右,產(chǎn)生的未知數(shù)較多,為解決電大尺寸問題帶來了困難。為了精確分析計(jì)算電磁學(xué)中電大尺寸散射問題,本文從基函數(shù)著手,實(shí)現(xiàn)了基于修正勒讓德多項(xiàng)式的高階基函數(shù)的高階矩量法。高階基函數(shù)定義在大尺寸的單元上,能有效地減少了未知量的個(gè)數(shù)。本文首先介紹電場積分方程和矩量法的基本原理,高階曲面插值,以及建立在曲面四邊形單元上的高階基函數(shù)。高階基函數(shù)由兩部分組成:棱邊基函數(shù)與面元基函數(shù)。棱邊基函數(shù)建立在公共棱邊的四邊形對上,保證了相鄰單元的電流法向的連續(xù),面元基函數(shù)則建立在單個(gè)四邊形面元上,對邊界處法向的電流沒有貢獻(xiàn)。為了減少阻抗矩陣的條件數(shù),本文著重分析了修正的勒讓德高階基函數(shù),該基函數(shù)在保證電流法向連續(xù)的條件下使得部分基函數(shù)具有正交性,減少了阻抗矩陣的條件數(shù),從而加快迭代求解速度。在基于修正勒讓德多項(xiàng)式的高階矩量法通用代碼的具體實(shí)現(xiàn)的過程中,首先利用了鄰接矩陣與關(guān)聯(lián)矩陣實(shí)現(xiàn)了離散四邊形單元的快速查找,介紹了高階曲面插值的一般過程,推導(dǎo)了阻抗矩陣填充的具體公式,采用Duffy變換解決了阻抗矩陣元素奇異性問題。最后,通過平板電流分布與任意形狀電磁散射問題檢驗(yàn)了高階矩量法的正確性與有效性。
[Abstract]:The RWG basis function is defined on the triangular pairs with common edges. The moment method based on the RWG basis function requires that the edge length of each triangulation is about 1/10 wavelength, which results in more unknowns. It is difficult to solve the problem of electrically large size. In order to accurately analyze and calculate the scattering problem of electrically large size in electromagnetics, this paper begins with the basis function. The method of moments of higher order basis functions based on modified Legendre polynomials is implemented. Higher order basis functions are defined on large size elements. In this paper, the basic principle of electric field integral equation and the method of moments, the interpolation of higher order surface, is introduced. Higher order basis functions are constructed on curved quadrilateral elements. Higher order basis functions consist of two parts: edge basis functions and plane basis functions. Edge basis functions are based on quadrilateral pairs of common edges. In order to reduce the condition number of impedance matrix, the surface element basis function is established on a single quadrilateral element and has no contribution to the normal current at the boundary. In this paper, the modified Legendre higher order basis function is analyzed, which makes the partial basis function orthogonal and reduces the condition number of impedance matrix under the condition that the current is normal and continuous. In the process of realizing the general code of high order moment method based on modified Legendre polynomials, the fast searching of discrete quadrilateral elements is realized by using adjacent matrix and correlation matrix. This paper introduces the general process of interpolation of high order surface, deduces the specific formula of filling impedance matrix, and solves the singularity problem of impedance matrix element by Duffy transform. The validity and validity of high order method of moments are verified by plate current distribution and electromagnetic scattering problem of arbitrary shape.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TN011

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本文編號(hào)：1536824