Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence 19 times faster than GMRES. The isolation and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES. The reflection and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

A Fast Finite Element Analysis of Millimeter Wave Waveguide Filters

The multifrontal method is applied for solving a large system of linear equations resulting from the use of edge-based finite element method (FEM). The finite element method combined with the perfectly matched layers (PML) is given for simulation of microwave filters and the algorithm of multifrontal method is described in detail. The reflection and insertion losses of millimeter wave filter are analyzed as the examples and the obtained results are compared with those obtained from literature. In order to demonstrate the efficiency of the multifrontal method, the computational time is compared with that of both symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) and conjugate gradient methods (CG) for the thick-iris waveguide bandpass filer.     

Simulation of Millimeter Wave Circulators by FEM with Unifrontal/Multifrontal Technique

The combination of unifrontal and multifrontal techniques is applied for solving a large, sparse, and unsymmetric system of linear equations resulting from the use of edge-based finite element method (FEM) for millimeter wave ferrite devices. The formulation of finite element method combined with the perfectly matched layers (PML) is given and the combined algorithm of unifrontal and multifrontal methods is described. The lower data movement of unifrontal method and the lower fill-in of normal multifrontal methods are combined for an algorithm with their features. The performance of typical waveguide junction circulators is analyzed and the calculated results are compared with those obtained from the literature.     

一种二阶混合有限体元格式的GAMG预条件子

针对一种含跳系数椭圆问题的二阶混合有限体元格式,讨论求解相应离散系统PGMRES法的预条件子构造问题.通过严格的理论分析,建立分层基下该二阶混合有限体元刚度矩阵和二次有限元刚度矩阵的谱等价关系,并利用关于二次有限元刚度矩阵的一种基于分层思想的GAMG预条件子,为二阶混合有限体元刚度矩阵设计一种高效GAMG预条件子.数值结果验证理论分析的正确性和新预条件子的高效性与稳定性.     

A kernel-free boundary integral method for elliptic boundary value problems

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.     

微波元件与加速结构的有限元分析

研究了有限元方法在二维均匀结构和轴对称加速结构中的应用,采用了带宽优化技术和子空间求解特征值方法,并给出了部分例子,结果表明该方法精度高、速度快.这些方法可直接用于三维程序、并行计算.     

有限元法求解任意折射率分布光纤模场分布

 应用有限元方法求解了任意径向非均匀折射率分布园柱对称介质波导中纵向场耦合波动方程定解问题所对应的变分问题,该方法不受弱导或高斯模场分布等限制,可方便地求解光纤中介质波导的模场分布。用此方法研究了带阶跃环的三角型分段折射率分布光纤中归一化模场半径与芯层传输功率比值随光纤不同结构参数的变化规律。     

光波导的自洽场计算Ⅱ.通道光波导

用自洽场（ＳＣＦ）法求通道光波导问题的解,得到了有１０位有效数字的传播常数,证明从精度上和时机上,自洽场法都远较有限元法（ＦＥＭ）优越,应该在高级的光波导设计中么应用。还详细讨论了自洽场能够高精度而有限元法最终不可能提高精度的原因。     

Design and analysis of coplanar waveguide optical modulator using finite element method

An analysis is given on the finite element method (FEM) for calculating the various parameters of optical modulators and a computer program is written to solve the finite element equation. Based on this method, a Mach-Zehnder type electro-optic modulator with coplanar waveguide (CPW) electrode is designed and fabricated. When compared with the Fourier series method, small differences on the 3-dB bandwidth, characteristic impedance and half-wave voltage, etc. are obtained.     

Non-iterative bi-directional wave propagation method for treating reflections

We describe a bi-directional wave propagation method based on the split-step non-paraxial collocation method. The method is non-iterative and does not require any matrix inversion or diagonalization. The method is applied to reflections from waveguide discontinuities, terminations as well as multilayer reflecting structures. The results obtained compare very well with those obtained using computationally intensive methods such as the finite element method (FEM) and the finite-difference time-domain (FDTD) method.     

Free Mesh Method: fundamental conception, algorithms and accuracy study

The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

求解辐射传递的非结构混合有限体积／有限元法

本文给了一种适用于任意非结构网格的有限体积/有限元法的混合算法用于求解多维半透明吸收、发射、散射性灰矩形介质内的辐射传递.该方法使用有限元法进行角度离散,有限体积法进行空间离散.与基于辐射传递离散坐标方程的方法不同的是,该方法在迭代求解的过程中,针对每一个空间体元,所有角度方向的辐射强度同时耦合求出.通过两个算例验证了该解法的正确性.     

A kernel-free boundary integral method for elliptic boundary value problems

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.     

Mode characteristics of nested eccentric waveguides constructed by two cylindrical nanowires coated with graphene

A kind of nested eccentric waveguide constructed with two cylindrical nanowires coated with graphene was designed. The mode characteristics of this waveguide were studied using the multipole method. It was found that the three lowest modes (mode 0, mode 1 and mode 2) can be combined by the zero-order mode or/and the first-order modes of two single nanowires. Mode 0 has a higher figure of merit and the best performance among these modes within the parameter range of interest. The mode characteristics can be adjusted by changing the parameters of the waveguide. For example, the propagation length will be increased when the operating wavelength, the minimum spacing between the inner and outer cylinders, the inner cylinder radius and the Fermi energy are increased. However, when the outer cylinder radius, the dielectric constants of region I, or the dielectric constants of region III are increased, the opposite effect can be seen. These results are consistent with the results obtained using the finite element method (FEM). The waveguide structure designed in this paper is easy to fabricate and can be applied to the field of micro/nano sensing.     

激光辐照受拉铝板破坏行为的时空多尺度数值模拟

推导耦合过渡区内参变量信息交换的元/网格动量传递多尺度算法,建立离散元与有限元耦合时空多尺度计算模型,并应用于激光辐照下受拉铝板破坏行为的数值模拟中.通过对比有限元计算模型、空间多尺度计算模型与时空多尺度计算模型在激光辐照下受拉铝板破坏算例的模拟结果,验证离散元与有限元耦合时空多尺度计算模型的准确性和数值计算高效率优势.使用该多尺度计算模型从宏观和细观尺度对铝板破坏行为进行数值模拟,模拟结果与实验结果基本一致.     

冲击动力学中离散元与有限元相结合的计算方法研究

 阐述了一种离散元与有限元法相结合的计算方法,编制了可应用于细观模拟的二维程序,对受冲击载荷作用的均匀材料和非均匀材料的响应特征进行了计算,并对数值模拟进行了验证。计算结果与理论值较吻合,验证了方法的可行性。     

相变温度场中无网格伽辽金法的应用

简述了无单元法的基础理论,推导出相变温度场的无单元法计算公式,采用罚函数法引入了第一类边界条件,编制了相应的计算程序.通过经典相变的应用例子,和有限元计算结果及解析解的比较,说明了无单元法应用于相变温度场具有连续性好,精度高,前后处理简单等优点.     

半解析对偶棱边元及其在波导不连续性问题中的应用

给出电磁波导的对偶变量变分原理,并采用对偶棱边元对波导的横截面进行半解析离散. 将波导中沿纵向均匀的区段视为子结构,运用基于Riccati方程的精细积分算法求出其出口刚度阵,然后与不均匀区段的常规有限元网格拼装即可对波导不连续性问题进行求解. 半解析对偶棱边元的采用可以在最大程度上对有限元网格进行缩减,并且能够在不增加计算量的前提下任意增加子结构的长度,从而可以将截断求解区域的人工边界设置在距离不均匀区段充分远的地方,极大地减少了近似边界条件所带来的误差. 数值算例证明这种方法具有很高的精度与效率. 关键词： 波导的不连续性 半解析辛分析 对偶棱边元 精细积分