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.     

Efficient Analysis of Millimeter Wave Ferrite Circulators by the GMRES Iterative Algorithm

The finite element method (FEM) combined with the perfectly matched layers (PML) is given for simulation of waveguide ferrite 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. The formulation of FEM and the algorithm of GMRES method are described in detail. The reflection and insertion losses of millimeter wave waveguide circulator are analyzed and the results are compared with those obtained from literature.     

Application of Robust Incomplete Cholesky Factorizations Preconditioned CG Algorithms for FEM Analysis of Millimeter Wave Filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.     

CAD of Millimeter Wave Y-Junction Circulators with a Ferrite Sphere

A gradient optimization technique along with a definition of cost function is applied to the CAD of the circulator with a magnetized ferrite sphere for millimeter wave communications. A three-dimensional Finite-Difference Time-Domain (FDTD) approach for the analysis of this ferrite sphere based microstrip circulator is presented. The topology of the structure is enforced at each step of optimization and its physical dimensions are used as optimization variables. The cost function is defined using location of zeros and poles of the circulator's transmission, isolation, and reflection functions. Numerical tests show that the optimization process converges from an arbitrarily selected starting point with the new definition of the cost function.     

Analysis of the H-Plane T-Junction Millimeter Wave Waveguide Circulator with a Ferrite Sphere

This paper presents an approximate but efficient field treatment of the new easy-to-fabricate ferrite sphere based H-plane waveguide circulator for potentially low-cost millimeter wave communication systems. A new three-dimension modeling strategy using a self-inconsistent mixed coordinates based mode matching technique is developed, i.e. the solutions of the Helmholz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical and general Cartesian modes respectively. The point matching method is then used on the interface to numerically obtain the coefficients of different orders basis functions of the field. Therefore, the field distributions as well as the characteristics of the circulator are numerically calculated and the good agreement is observed between the numerical results and the measured data.     

Fast Stimulation of Millimeter Wave Waveguide Filters by Boundary Marching Method

The boundary marching method is applied for the analysis of the waveguide bandpass filers. The vector finite element method with the perfectly matched layers (PML) as the matching load is given for parameter extraction of millimeter wave filters. The implementation of the fast boundary marching method is described in detail. The reflection and insertion losses of millimeter wave filters are obtained and compared with those obtained from literature.     

Development of the Microstrip Circulator with a Magnetized Ferrite Sphere in Millimeter Wave Band

In this paper, a novel microstrip circulator with a magnetized ferrite sphere is proposed for various millimeter wave communications. A three-dimensional Finite-Difference Time-Domain (FDTD) approach for the analysis of this ferrite sphere based microstrip circulator is first presented. The electromagnetic fields inside the ferrite junction are calculated using special updating equations derived from the equation of motion of the magnetization vector and Maxwell's curl equations in consistency. Frequency dependent insertion loss, isolation and reflection loss of circulator are calculated over a wide band of frequencies with a single FDTD run. Experimental results at Ka band are presented and compared with theoretical simulations. As a result, a good agreement is found between them.     

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.     

A compound high power millimeter wave waveguide circulator

In this paper, a high power millimeter wave waveguide Y-junction circulator, which is compound in structure, has been analyzed and developed. Its enduring power attains 60 W CW-power and the temperature of the waveguide surface does not exceed 25 degree centigrade under natural coolness.     

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.     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

GMRES算法在二维定常无粘流计算中的应用

发展了GMRES算法的两种不同预处理方法求解二维无粘流体动力学方程组。在保证计算效率的基础上,采用了一种减小内存需求的途径。用两个算例对GMRES算法以及两种不同的预处理方法进行分析,同时与DDADI方法进行比较。通过对NACA0012有攻角超临界流动以及GAMM通道超音流的计算,表明两种预处理下的GMRES算法都具有收敛速度快的优点,LUSGS预处理方法略优于ILU预处理方法。     

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.     

Analysis of Antennas with PBG Substrate

The use of photonic materials has been used in the theory of optical waves. The PBG (Photonic Band Gap) theory and material, was developed recently for optical frequencies and can be easily applied to millimeter waves, microwaves and planar antenna frequencies. The presence of photonic materials as substrate in antennas has some good characteristics such as, supression of light spontaneous emission and suppression of surface waves, allowing the application in planar antenna array. In this work an elaborate analysis using the full wave Transverse Transmission Line - TTL method, that provides efficient and concise results is applied to the planar antennas array with PBG substrate.     

Full-Wave Analyses of Coaxial to Waveguide Adapters by the FDTD Method

The finite-difference time-domain (FDTD) method is applied to the full-wave analyses of the electrical properties of millimeter wave coaxial to waveguide adapters. The results are useful for the design of wideband coaxial to waveguide adapter.     

Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.     

H-plane cross-shaped waveguide circulator in magneto-photonic crystals with five ferrite posts

A novel H-plane cross-shaped circulator based on magneto-photonic crystals is experimentally investigated.The band gap of the TE mode for the photonic crystals is calculated by the plane wave expansion method.The transmission characteristics of the circulator are simulated by the finite element method.We perform the experiments in the microwave regime to validate the numerical results.At the central frequency of 10.15 GHz,the measured isolation and insertion loss of the circulator reaches-30.2 and-3.93 d B,respectively.The bandwidth of the circulator is about 550 MHz.The optimal experimental value of isolation is higher than the numerical value.     

Characteristics of millimeter wave detection in a Fabry-Perot resonator using a YBCO-BiO composite superconductor

A quasioptical technique with a hemispherical-type Fabry-Perot resonator for measuring characteristics of millimeter wave detection using a YBCO-BiO composite superconductor has been successfully developed. This Fabry-Perot resonator consists of a spherical mirror and a plane mirror mounted on the cold head of the refrigerator, under a controlled temperature of 40 to 300 K. The method offers the advantages of estimating irradiation power, easily controlling the sample temperature, analyzing the mode of the irradiated millimeter waves and easily extending to higher frequencies. The superconducting millimeter wave detector has been measured with this technique, with measured sensitivities of 46.5 V/W (70 K) to 160 V/W (35 K) at 50 GHz. These results are close to the theoretical values calculated numerically from the characteristics of the detector. It was confirmed that the millimeter wave detection system using the Fabry-Perot resonator is suitable for estimating the sensitivity of the high-Tc superconducting millimeter wave detector.     

Discussion About the Ratio Method for Measuring Millimeter Wave Absorption by Biological Entities

An attempt to measure millimeter wave absorption spectra of E. coli was performed with a commonly used ratio method. The influences of water, which absorbs millimeter wave strongly, and the thickness of a sample holder were greatly reduced in our measurement compared with former reports. Some resonance-like absorption spectra were observed, but the resonance was found not from the absorption by E. coli after carefully examining the measurement. The reasons giving rise to the resonance-like artifacts were discussed. Proposals for making better use of the ratio method are given.     

Millimeter wave microstrip circulator

A new and unique microstrip drop-in type Y-junction circulator has been designed and developed for operation in the millimeter wave frequency region. This device utilizes NiZn ferrite as the gyromagnetic material which is mounted on a duroid substrate.