基于修正勒让德多项式高阶基函数的矩量法研究

发布时间：2018-02-26 06:12

本文关键词： 高阶矩量法高阶基函数棱边基函数面元基函数修正勒让德多项式高阶基函数高阶曲面建模　出处：《南京邮电大学》2015年硕士论文　论文类型：学位论文

【摘要】：RWG基函数定义在具有公共棱边的三角形对上,建立在RWG基函数上的矩量法要求剖分的每个三角形的边长在十分之一波长左右,产生的未知数较多,为解决电大尺寸问题带来了困难。为了精确分析计算电磁学中电大尺寸散射问题,本文从基函数着手,实现了基于修正勒让德多项式的高阶基函数的高阶矩量法。高阶基函数定义在大尺寸的单元上,能有效地减少了未知量的个数。本文首先介绍电场积分方程和矩量法的基本原理,高阶曲面插值,以及建立在曲面四边形单元上的高阶基函数。高阶基函数由两部分组成:棱边基函数与面元基函数。棱边基函数建立在公共棱边的四边形对上,保证了相邻单元的电流法向的连续,面元基函数则建立在单个四边形面元上,对边界处法向的电流没有贡献。为了减少阻抗矩阵的条件数,本文着重分析了修正的勒让德高阶基函数,该基函数在保证电流法向连续的条件下使得部分基函数具有正交性,减少了阻抗矩阵的条件数,从而加快迭代求解速度。在基于修正勒让德多项式的高阶矩量法通用代码的具体实现的过程中,首先利用了邻接矩阵与关联矩阵实现了离散四边形单元的快速查找,介绍了高阶曲面插值的一般过程,推导了阻抗矩阵填充的具体公式,采用Duffy变换解决了阻抗矩阵元素奇异性问题。最后,通过平板电流分布与任意形状电磁散射问题检验了高阶矩量法的正确性与有效性。
[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.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011

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