B样条有限元法解波导体征值问题

本文引入Ｂ样条有限元法计算波导本征值问题。该方法不但计算精度高，而且能保证场量横向分量应有的连续性。文中首先建立求解波导本征值问题中的Ｂ样条有限元方程，然后介绍矩阵元素的计算方法，最后通过两个典型算例计算，表明方法的应用特点和价值。     

B样条有限元法解波导本征值问题

本文引入Ｂ样条有限元法计算彼导本征值问题．该方法不但计算精度高，而且能保证场量横向分量应有的连续性．文中首先建立求解波导本征值问题中的Ｂ样条有限元方程，然后介绍矩阵元素的计算方法，最后通过两个典型算例计算，表明方法的应用特点和价值．     

矩—圆同轴波导的高次模特性

本文将正交展开法和伽略金（Ｇａｌｅｒｋｉｎ）法相结合，提出了用于矩－圆（Ｃ－Ｒ）波导高次本征模的精确分析法，采用贝塞尔－傅立叶级数把这种分析法中使用圆形和矩形坐标系合并起来，高次模的截止频率由奇异值分解（ＳＶＤ）法来确定，计算结果与使用有限元获得的结果相当一致，因为有解析形式的解，因此，本文法对于许多实际微波元件和电路分析都是有用的。     

波导本征值问题的多极理论分析

本文利用多极理论分析波导本征值问题.给出用多极理论分析波导本征值问题的使用规则和实施方法.实例计算结果表明,用多极理论分析波导本征值问题,不仅具有较高的计算精度,而且可以很方便地应用于波导工程问题的设计与计算,多极理论是一种有效的波导本征值分析方法.     

弯波导的本征模与角传播常数

本文采用严格的本征模表示矩表截面均匀弯曲波导中的场，文中给出了虚阶Ｂｅｓｓｅｌ函数及其导数的计算公式和计算方法，由此完整地解决了任意半径弯波导本征征模及角传播常数的精确计算问题，典型数值计算结果表明，弯波导中的本征模与直波导中的本征模具有一一对应关系，变波导的等效传播常数与直波导的传播常数在数值上相当接近，模场的径向分布则呈衰减的驻波形式。     

部分填充各向异性介质波导的有限元分析

本文用有限元方法分析了部分填充各向异性介质波导的本征值问题。首先推导了电磁场的变分表示式,然后用有限元方法将此式进行离散,得出广义代数本征值问题,并编制出计算机程序,求出问题的数值解。文中给出了部分填充圆形和矩形杆状各向异性介质的矩形金属波导的色散曲线和场分布图的计算结果,对于矩形介质杆情形,与用其它方法所得结果作了比较。     

矩-圆同轴波导的高次模特性

本文将正交展开法和伽略金(Galerkin)法相结合,提出了用于矩-圆(C-R)波导高次本征模的精确分析法。采用贝塞尔-傅立叶级数把这种分析法中使用的圆形和矩形坐标系合并起来。高次模的截止频率由奇异值分解(SVD)法来确定,计算结果与使用有限元法获得的结果相当一致。因为有解析形式的解,因此,本方法对于许多实际微波元件和电路的分析都是有用的。     

波导本征问题分析的径向基函数方法

 针对网格方法分析波导本征问题时常面临剖分和近似精度低的问题,论文将基于配点原理的径向基函数无网格方法引入进来.给出径向基函数法求解本征值问题的方法、实施步骤和相应的离散方程形式.以矩形、圆形和L形波导的本征分析为例,通过与有限元法比较,反映该方法具有计算量小和精度高的优势,另外,它实施方便并易于推广到高维问题中.     

波导加载腔的场计算

本文基于边界元法（ＢＥＭ），提出了一种新的计算波导加载谐振腔的谐振频率，外Ｑ值和场分布的数值计算方法，计算表明，用ＢＥＭ来处理波导加载腔这样的开放系统。具有计算时间短，机器内存少和精度高等优点。     

非对称三层钇铁石榴石薄膜光波导的模传输特性

通过液相外延法（ＬＰＥ），首先在钆镓石榴石（ＧＧＧ）基片（ＩＩＩ）晶面上生长ＣｏＹＩＧ薄膜，然后连续生长双层（ＢｉＡｌ）ＹＩＧ薄膜，制备出非对称三层钆铁石榴石薄膜波导，推导出这种结构的波导的波导层、缓冲层和吸收层模式的本征方程，以及微分法计算模吸收系数的公式。用这些方程计算了波导层模式的截止厚度和基模的有效折射率，以及波导层、缓冲层和吸收层模式的模吸收系数。     

Higher order large-domain FEM modeling of 3-D multiport waveguide structures with arbitrary discontinuities

A highly efficient and accurate higher order large-domain finite-element technique is presented for three-dimensional (3-D) analysis of N-port waveguide structures with arbitrary metallic and dielectric discontinuities on standard PCs. The technique implements hierarchical polynomial vector basis functions of arbitrarily high field-approximation orders on Lagrange-type curved hexahedral finite elements of arbitrary geometrical orders. Preprocessing is carried out by a semiautomatic higher order meshing procedure developed for waveguide discontinuity problems. The computational domain is truncated by coupling the 3-D finite-element method (FEM) with a two-dimensional (2-D) modal expansion technique across the waveguide ports. In cases where analytical solutions are not available, modal forms at the ports are obtained by a higher order 2-D FEM eigenvalue analysis technique. The examples demonstrate very effective higher order hexahedral meshes constructed from a very small number of large curved finite elements (large domains). When compared to the existing higher order (but small domain) finite-element solutions, the presented models require approximately 1/5 of the number of unknowns for the same (or higher) accuracy of the results.     

波导本征值问题的有限元分析

本文简要讨论了波导本征值问题的有限元分析方法。给出了一个用有限元法求解波导本征值问题的标准程序。使用该程序可以获得一大类横截面周界由直线及圆弧围成的波导的各个本征值和本征函数。文中通过对十几种不同结构波导本征值问题的求解,证实了该程序的可靠性。     

NURBS在自适应hp有限元分析系统中的应用

在传统的有限元分析中,对于曲边区域或者曲边的分界面并没有很好的近似方法,通常使用大量的线性单元近似的描述曲边计算区域.这些新增加的单元不仅浪费了计算时间,而且往往并不是需要求解的部分.采用曲线单元可以避免对单元的强制细化,有效的提高计算的精度.曲边单元使用非均匀有理B样条（NURBS）曲线实现,可以有效的消除几何离散误差,保证整体的高阶连续性.详细讨论了基于NURBS曲线的自适应三角形网格剖分和四边形网格剖分,并结合自适应hp有限元算法解决实际问题.从计算自由度和计算时间的角度比较典型的工程算例结果,采用NURBS曲边单元的hp有限元算法能够很好的消除几何近似导致的误差,提高计算的效率.     

An analysis of the scalar Helmholtz equation using the integralequation method

The scalar Helmholtz equations are investigated by using the integral equation method (IEM). In the IEM analysis, the fundamental solution of the Laplace equation is used as a weighting function. Two IEM formulations are obtained: one is a standard formulation and the other is obtained from an elimination of the unknown boundary value. The accuracy and computational time of the IEM are compared with those of the finite element method in two dimensional scalar Helmholtz problems. The analysis of a resonant cavity is reduced to a simple eigenvalue problem. Resonant frequencies of the IEM agree well with those of the finite difference method. Usefulness of the IEM is confirmed through the analyses of the scalar Helmholtz equations     

The computational performance of a high-order coupled FEM/BEMprocedure in electropotential problems

This paper presents a thorough analysis of the computational performance of a coupled cubic Hermite boundary element/finite element procedure. This C1 (i.e., value and derivative continous) method has been developed specifically for electropotential problems, and has been previously applied to torso and skull problems. Here, the behavior of this new procedure is quantified by solving a number of dipole in spheres problems. A detailed set of results generated with a wide range of the various input parameters (such as dipole orientation, location, conductivity, and solution method used in each spherical shell [either finite element or boundary elements]) is presented. The new cubic Hermite boundary element procedure shows significantly better accuracy and convergence properties and a significant reduction in CPU time than a traditional boundary element procedure which uses linear or constant elements. Results using the high-order method are also compared with other computational methods which have had quantitative results published for electropotential problems. In all cases, the high-order method offered a significant improvement in computational efficiency by increasing the solution accuracy for the same, or fewer, solution degrees of freedom.     

Finite element beam propagation method for three-dimensionaloptical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide     

Modeling three-dimensional discontinuities in waveguides usingnonorthogonal FDTD algorithm

A generalization of the finite-difference time-domain (FDTD) algorithm adapted to nonorthogonal computational grids is presented and applied to the investigation of three-dimensional discontinuity problems. The nonorthogonal FDTD uses a body-fitted grid for meshing up the computation domain and, consequently, is able to model the problem geometry with better accuracy than is possible with the staircasing approach conventionally employed in the FDTD algorithm. The stability conditions for the nonorthogonal FDTD algorithm are derived in two an three dimensions. Numerical results, including an H-plane waveguide junction, a circular waveguide with a circular iris, a circular waveguide with a rectangular iris, and a microstrip bend discontinuity, are presented to validate the approach     

A wide-angle finite element beam propagation method with perfectlymatched layers for nonlinear optical waveguides

A beam propagation method (BPM) based on the finite element method (FEM) is described for the analysis of both transverse electric (TE) and transverse magnetic (TM) waves propagating in nonlinear optical waveguides. A perfectly matched layer is introduced to avoid spurious reflections from computational window edges. For the wide-angle beam propagation analysis, the Pade approximation is introduced to the differential operator along the propagation direction. In order to improve numerical accuracy and efficiency, a finite element mesh and a reference refractive index are adaptively renewed at each propagation step, and to reduce computational effort for the nonlinear optical waveguide analysis, an iterative algorithm is also introduced. Waveguides with nonlinear self-focusing claddings are analyzed to investigate spatial soliton emission phenomena, and it is confirmed that soliton couplers can be easily constructed     

Efficient analysis of waveguide components using a hybrid PEE-FDFD algorithm

The partial eigenfunction expansion (PEE) method combined with the classical finite difference frequency domain (FDFD) algorithm is proposed to accelerate frequency domain analysis of waveguide components. Examples are shown validating the method both for eigenvalue and deterministic problems.