Edge-based Finite Element Research Articles

Investigation of numerical precision of 3-D RFECT signal simulations

This paper evaluates the numerical precision of a three-dimensional A/sub r/ method with edge-based finite elements in the simulation of remote field eddy-current testing of a ferromagnetic tube. The method is employed with a suitable formula for the electromotive force signal calculation in magnetic materials. Using a supercomputer, analyses of the mesh division effect on numerical precision are carried out to find out the proper mesh conditions for signal simulations of 3-D defects. Good agreements of the simulated signals with experimental ones are obtained using this method with an acceptable computational resource. In this way, the 3-D simulation of remote field eddy-current testing signals for a magnetic tube has become possible in practical applications.

Comparison of geometric and algebraic multigrid methods in edge-based finite-element analysis

This paper discusses the comparison between the geometric multigrid (GMG) method and the algebraic multigrid (AMG) method in edge-based finite-element (FE) analysis. The GMG method requires the hierarchical meshes. On the other hand, the AMG method requires the only a single mesh information. The system matrices of the coarse grids are generated using algebraic operation in AMG. The numerical results show that both multigrid methods are faster than the conventional solvers in large-scale analysis. Although multigrid methods require the setup procedures, the calculation time of these procedures is comparatively short and increase linearly with the number of unknowns.

Examination of Electromagnetic Inspection of Surface Hardness: 3-D Nonlinear FEM Analysis Considering Nonuniform Permeability and Conductivity

The inspection of surface hardness of the hardened steel is important in keeping the quality of automobile parts, etc. The permeability of hardened steel decreases when the hardness is increased. Therefore, the surface hardness evaluation is possible by detecting the difference of the magnetic characteristic using the electromagnetic inspection method. However, the surface hardness inspection is not easy, because the relative permeability and conductivity of the hardened steel are usually nonuniform compared with that of the normal steel. In this paper, the technique for reducing the effect of the nonuniformity of the permeability and the conductivity on the large magnetic noise, and measuring the surface hardness is examined using three-dimensional edge-based hexahedral finite element method. In addition, the experimental verification is also carried out.

Analysis of Writing Characteristics of CF-SPT Head Using 3-D Read/Write Simulation System

Recently, the increase of areal recording density is remarkable. In order to develop a high density recording device, a read/write (R/W) simulation using three dimensional (3-D) magnetic field analysis is indispensable. In this paper, the magnetic field in a cusp-field single-pole-type (CF-SPT) head with discrete track media is analyzed using a 3-D R/W simulation system, in which edge-based finite element method and 3-D medium hysteresis model based on the ensemble of the Stoner-Wohlfarth (SW) particles are combined. The effects of ampereturns and the discrete track media on the distribution of recorded magnetization are investigated. The detailed behavior of flux around the discrete track media and continuous media is illustrated.

Robustness of the multigrid method for edge‐based finite element analysis

AbstractThe dependence of the multigrid finite element method solving three‐dimensional magnetostatic fields on the quality of the finite element mesh is reported. It is shown that the convergence of the multigrid method is strongly influenced by the mesh quality. Moreover, the multigrid method with ICCG smoother is shown to be more robust against mesh distortion than that with Gauss–Seidel and SOR smoothers. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 148(1): 75–81, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10289

Three-Dimensional Defect Reconstruction From Eddy-Current NDE Signals Using a Genetic Local Search Algorithm

This paper introduces a model-based approach to reconstruct three-dimensional defect profiles from eddy-current nondestructive evaluation signals. The method casts the defect characterization problem as an exercise in maximization of an appropriate cost function. The method uses an edge-based finite-element forward model to simulate the underlying physical process and a genetic search algorithm to solve the optimization (maximization) problem. The paper presents techniques to reduce the computation cost for evaluating the cost function as well as local search methods to speed the genetic search process. Test results confirm the validity of the approach.

Edge‐based finite‐element analysis of the field patterns in V‐shaped microshield line

AbstractIn this paper, field patterns in V‐shaped microshield transmission line are calculated by using the edge‐based finite element method. The dependence of the field patterns upon the thickness of metallic signal strip and the dielectric constant of dielectric substrate is presented. The figures in this paper have important values in the design of microshield lines in microwave and millimeter‐wave integrated circuits. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 41: 43–47, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20041

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.

ＳＰＴヘッド／２層膜媒体系における隣接トラックからの影響

The perpendicular stray field from the tracks neighboring the center track in a perpendicular SPT head/double-layer medium system was investigated using a 3D read/write simulation system in witch the Poisson equation for the head/medium system is solved by the edge-based finite element method. The main results were as follows: (1) the stray field in the double-layer medium is about two times greater than that in the single layer, (2) the stray field under the main pole or the auxiliary pole in an SPT head as a function of the relative permeability μr of a soft underlayer (SUL) initially increases, reaches a maximum at around μr = 10, and decreases monotonically with increasing μr, (3) the stray field for SUL μr greater than 10 is increased by cutting tha SUL into short tracks, and (4) the stray field is almost independent of the thickness of the SUL when μr is greater than 100.

W Band Circular Waveguide Y-Junction Circulator

In this paper, a new type of W band circular waveguide Y-junction circulator is presented. The structure of this type of Y-junction is a cylindrical cavity connecting with three circular waveguides. The performances of the type of circulator are analyzed by the edge-based vector finite element method hybridized with the modal expansion. The numerical results show that this type of waveguide Y junction circulator has good circulation performance.

Waveguide matching crossed-slot

A matching crossed-slot, which is accommodated at the shorted end of a waveguide crossed-slot array and radiates all the residual power with circular polarisation in an array beam direction, is analysed and designed by the method of moments (MoM). The eigenmode functions for a crossed-slot derived numerically by the edge-based finite element method (FEM) are utilised as the basis functions in the MoM. The mechanism of circular polarisation is interpreted in terms of two modes each radiating linear polarisation. A matching crossed-slot is designed and tested at 3.6 GHz. The measured reflection is suppressed below -15 dB over a 5.6% bandwidth from 3.5 GHz to 3.7 GHz. The calculated and measured axial ratios in a direction of 50 degrees are 0.32 dB and 1.5 dB, respectively.

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.

Analysis of ferrite waveguide devices by use of the edge FEM combined with the SOC technique

In this paper, ferrite waveguide devices are analysed by use of the edge-based vector finite element method combined with the short–open calibration (SOC) technique. The formulation with both permittivity and permeability tensors for tetrahedral vector elements is analytically given in terms of the electric field. The SOC technique is directly accommodated in the FEM algorithm and used to truncate the computational domain. The SOC technique removes or separates unwanted parasitics obtained by the approximation of the impressed voltage source and the inconsistency between different simulations. Several types of ferrite waveguide device are analysed and the results are compared with those of the available publications. A good agreement is observed 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.

Edge-based finite element approach to the simulation of geoelectromagnetic induction in a 3-D sphere

We present a new simulator based on an edge‐based finite element method (FEM) for computing the global‐scale electromagnetic (EM) induction responses in a 3‐D conducting sphere excited by an external source current for a variety of frequencies. The formulation is in terms of the magnetic vector potential. The edge‐element approach assigns the degrees of freedom to the edges rather than to the nodes of the element. This edge‐element strictly satisfies the discontinuity of the normal boundary conditions without considering the enforced normal boundary conditions that are usually practiced in a node‐based FEM. To verify our simulation code, we compare our results with those of other solvers for two test computations, corresponding to azimuthally symmetric and asymmetric models. The results are in good agreement with one another.

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.

Edge‐based finite element method for shallow water equations

AbstractThis paper describes an edge‐based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non‐linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi‐discrete and space–time analyses. Stabilized formulations, including Petrov–Galerkin models and discontinuity‐capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge‐based approach are presented at the end of the paper. Copyright © 2001 John Wiley & Sons, Ltd.

Edge‐based finite element techniques for non‐linear solid mechanics problems

AbstractEdge‐based data structures are used to improve computational efficiency of inexact Newton methods for solving finite element non‐linear solid mechanics problems on unstructured meshes. Edge‐based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix–vector products needed in the inner iterative driver of the inexact Newton method. Numerical experiments on three‐dimensional plasticity problems have shown that memory and computer time are reduced, respectively, by factors of 4 and 6, compared with solutions using element‐by‐element storage and matrix–vector products. Copyright © 2001 John Wiley & Sons, Ltd.

Vector-FEM Analysis of Millimeter Wave Circulator with SOC Truncation Technique

In this paper, the application of the edge-based vector finite element method combined with the short-open calibration (SOC) technique to waveguide junction circulators was presented. By applying permittivity and permeability tensors, the functional formula for tetrahedral vector elements are analytically derived in terms of the electric field strength. And the SOC technique is directly accommodated in the FEM algorithm and used to truncate the computational domain. The SOC technique removes or separates unwanted parasitics brought by the approximation of the impressed voltage source and also the problem of resulting inconsistency between different simulations. Truncation of computational domain by SOC technique makes the iterative solvers for large-sparse linear matrix equations from FEM converge much faster than by perfectly matching layers (PML). The analysis of three 2-port networks is sufficient to form the admittance matrix of the corresponding three-port waveguide junction circulators. To validate the theory, typical three-dimensional numerical results of isotropic dielectric-filled discontinuity are first presented and compared with other hybrid numerical techniques. Further, the ferrite filled waveguide junction circulators are analysed and compared with the measured and available publications. The comparison shows that good agreement is obtained.

Efficient Analysis of Millimeter Wave Circuit Using Numerical Calibration Technique

In this paper, A numerical technique, called short-open calibration (SOC), in conjunction with edge-based finite element method (FEM) is employed to analyze millimeter wave circuit that can be segmented into two distinct section: static model of feedlines and dynamic model of circuit discontinuity. The derivation of reflection coefficient of 3D discontinuities is arranged in two steps. In the first step, this SOC technique is incorporated into the FEM for mesh truncation of computaional domain. In this way, much faster convergence is achieved for large-sparse linear matrix equations from FEM by this termination than by perfectly matching layers (PML). The field distribution of the dominated mode in uniform feedlines and entire circuit is obtained individually by exciting a pair of even and odd impressed voltages along the struture. In step two, Scattering parameters based on the voltages and current defintion is calculated by integral of electric and magnetic fields. Numerical solutions for a class of planar circuit discontuities are very well compared with those published in the available literatures.