Carter's factor calculation using domain transformations and the finite element method

The main purpose of this work is to present a methodology to calculate Carter's factor using the actual air‐gap geometry, that is, without simplifications of the slot geometry. The methodology is based on the finite element method, and its results are compared with some traditional procedures used for Carter's factor calculation and also with a domain transformation technique. It is shown that the finite element method and the domain transformation methodologies present similar results, which are different from the results obtained with traditional procedures. Copyright © 2011 John Wiley & Sons, Ltd.     

有限元一解析结合解法在无界轴对称静电场问题数值解中的应用

无界电磁场问题的有限元数值分析研究有着重要的理论意义和实用价值.本文采用有限元-解析结合解法实现了有限元法在无界轴对称静电场问题数值分析中的应用,并兼顾了计算精度和效率,形成了一种新型解法.以典型的静电场问题为例,说明了有限元-解析结合解法精度高、简单易行和方便直观,具有实用价值.同时,还保留了有限元法的固有优点.     

Large‐scale magnetic field analysis by the hybrid finite element‐boundary element method combined with the fast multipole method

This paper describes a large‐scale magnetic field analysis by means of the hybrid finite element‐boundary element (FE‐BE) method. The hybrid FE‐BE method is well‐suited for solving open electromagnetic field problems that comprise movement, nonlinear media, and eddy current. In general, however, large memory and computational costs are required due to the dense blocks in the system matrix generated by the BE part of the hybrid formulation. In order to overcome the above difficulties, we introduce the fast multipole method (FMM) to the hybrid FE‐BE formulation developed by ourselves. Furthermore, we propose a novel preconditioning technique suitable for the hybrid FE‐BE method with the FMM. Some numerical results that demonstrate the effectiveness of the proposed approach are also presented. ©2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(1): 73–80, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20508     

Analysis of quadruple corner‐cut ridged square waveguide by hybrid mode‐matching boundary‐element method

In this paper, the square waveguide with quadruple corner‐cut ridges is analyzed using the hybrid mode‐matching boundary‐element method. Because of its symmetry, only a quarter of its cross‐section needs to be considered and it is then divided into three regions. The electromagnetic field components in two regular regions can be obtained using the mode‐matching method and the third irregular region is discretized using the boundary‐element method. The combination of two methods produces one matrix equation, from whose determinant the cutoff wavenumbers of waveguide modes can then be computed. This hybrid technique takes advantage of the mode‐matching method's high efficiency and the boundary‐element method's versatility. The convergence of this hybrid method is studied, and numerical results are compared with the conventional boundary‐element method and commercial finite‐element software package, which shows that our hybrid method can achieve the same accuracy with much less time. The influence of the cut‐corners on the cutoff wavenumbers of the dominant and higher‐order modes is then examined. A simple approximate equation is found to accurately predict the cutoff wavenumber of TE₂₀ mode. The single‐mode bandwidth of a quadruple ridged square waveguide is calculated thereafter, which shows that this corner‐cut structure can provide a broader bandwidth compared to the one without cut‐corners. Copyright © 2010 John Wiley & Sons, Ltd.     

屏蔽电缆参数计算及屏蔽层与芯线间的串扰

为分析线缆间的串扰问题,基于有限元软件ANSYS分析了屏蔽电缆周围的电磁场分布,通过计算导体所带电荷量以及磁链,求得了多导体传输线系统的电感电容矩阵。针对位于地面上方的屏蔽电缆系统提出了一种新的表示其传输线参数的模型,即以大地为参考导体,建立包括芯线、屏蔽层、大地的统一模型,计算其相应的传输线参数;运用所得屏蔽电缆的传输线参数,结合传输线时域有限差分(FDTD)法,仿真分析了屏蔽电缆屏蔽层中的电压、电流在电缆芯线中的耦合响应问题;基于实验室研究设备,对同轴电缆屏蔽层与芯线之间的耦合问题进行了实验测量,验证了理论研究的正确性。     

An interface‐enriched generalized finite element analysis for electromagnetic problems with non‐conformal discretizations

An interface‐enriched generalized finite element method is presented for analyzing electromagnetic problems involving highly inhomogeneous materials. To avoid creating conformal meshes within a complex computational domain and preparing multiple meshes during optimization, enriched vector basis functions are introduced over the finite elements that intersect the material interfaces to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the sub‐elements. Several numerical examples are presented to verify the method with analytical solutions and demonstrate its h‐refinement convergence rate. The proposed interface‐enriched generalized finite element method is shown to achieve the same level of accuracy as the standard finite element method based on conformal meshes. Two examples, involving multiple microvascular channels and circular inclusions of different radii, are analyzed to illustrate the capability of the proposed approach in handling complicated inhomogeneous geometries. Copyright © 2015 John Wiley & Sons, Ltd.     

Role of the temperature distribution on the PN junction behaviour in the electro‐thermal simulation

Electro‐thermal simulations of a PIN‐diode based on the finite‐element method, show a non‐uniform temperature distribution inside the device during switching transients. Hence, the implicit assumption of a uniform temperature distribution when coupling an analytical electrical model and a thermal model yields inaccurate electro‐thermal behaviour of the PIN‐diode so far. The idea of including non‐uniform temperature distribution into power semiconductor device models is not new, as accurate electro‐thermal simulations are required for designing compact power electronic systems (as IC or MCM). Instead of using a one‐dimensional finite difference or element method, the bond graphs and the hydrodynamic method are utilized to build an electro‐thermal model of the PIN‐diode. The results obtained by this original technique are compared with those obtained by a commercial finite‐element simulator. The results are similar but the computation effort of the proposed technique is a fraction of that required by finite‐element simulators. Moreover, the proposed technique may be applied easily to other power semiconductor devices. Copyright © 2004 John Wiley & Sons, Ltd.     

An accurate time‐domain model of transmission lines with frequency‐dependent parameters

Linear lossy two‐conductor transmission line can be modelled as dynamic two ports in the time domain, via the describing input and transfer impulse responses. This convolution technique is very effective when dealing with networks composed of transmission lines with frequency‐dependent parameters and non‐linear and/or time‐varying circuits. The paper carries out an accurate analysis of this model, in the most general case of lines with frequency‐dependent parameters. For such lines it is not possible to evaluate analytically the impulse responses, nor is it possible to catch them numerically, due to the presence of irregular terms, such as Dirac pulses, terms that numerically behave as Dirac pulses, and functions of the type 1/t^ρ with 0 < ρ <1. A simple method is proposed to evaluate exactly all the irregular terms of the impulse responses: once these irregular parts have been extracted, the regular remainders are easily evaluated numerically. This method is applied to analyse lines with frequency‐dependent parameters of practical interest, such as superconductor transmission lines, power lines above a finite conductivity ground, lines with frequency‐dependent dielectric losses and lines with normal and anomalous skin‐effect. Numerical simulations are carried out for illustration. Copyright © 2000 John Wiley & Sons, Ltd.     

2D‐DOA estimation performance using split vertical linear and circular arrays

This paper presents a new approach to reduce the computational complexity in two‐dimensional (2D) matrix pencil (MP) method for direction of arrival (DOA) estimation of plane wave signals using a combination of vertical uniform linear array (VULA) and uniform circular array (UCA). By applying phase mode excitation based beamforming to the UCA, we can apply the matrix pencil (MP) method to the beamspace data using only a single snapshot. The technique is based on the split array, which is composed of two perpendicular arrays. The vertical uniform linear array used to determine the elevation DOA components is located perpendicularly at the center of the uniform circular array in the horizontal plane used to calculate the azimuth angles. Unlike common planar and circular arrays, this antenna array with its particular geometry requires no pair‐matching between the azimuth and the elevation angle estimation and can also remove the drawbacks of estimation failure problems. Using this particular geometry for the 2D MP method leads to an efficient computational methodology for real‐time implementation on a digital signal processor. The obtained simulation results of the MP method applied to both uncorrelated and correlated narrow‐band sources in the presence of white noise show good performance estimation. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Comparison between line and surface integral formulations of the hybrid mode‐matching/two‐dimensional finite element method

The hybrid mode‐matching/two‐dimensional‐finite‐element (MM/FEM2D) technique has been proposed for the analysis of discontinuities with waveguides of arbitrary cross section; this technique combines the computational efficiency of modal analysis with the versatility and flexibility of the FEM approach. In this paper, we present in detail a surface‐integrals and a line‐integrals formulation of the hybrid MM/FEM2D technique, in case the ‘Standard Formulation’ is used as FEM2D formulation. Such formulations allow computing analytically both the normalization and the coupling integrals. Furthermore, we compare the accuracy obtained by using the line‐integrals and the corresponding surface‐integrals formulation. To these aims we present several numerical results. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient analysis of planar microwave circuits with mixed‐order prism vector finite macroelements

This paper introduces a new concept of a mixed‐order prism macroelement, suitable for an efficient analysis of three‐dimensional planar microwave circuits, using two‐dimensional meshes and preprocessors. The mixed‐order concept used here implies arbitrary orders of variation in different directions and differs essentially from the well‐known mixed‐order approximation that is an integral part of every Whitney element. It is the existence of a related systematic theory of higher‐order vector finite elements, previously documented, that facilitates the introduction of such a concept. The second‐ and third‐order elements, derived by this approach, are successfully applied in the analysis of planar microwave circuits, rendering the application of finite element method in such problems still a favorable option. Copyright © 2008 John Wiley & Sons, Ltd.     

Least squares spectral element method for 2D Maxwell equations in the frequency domain

We propose a high order numerical method for the first order Maxwell equations in the frequency domain, defined in media with arbitrary complex shape. Our approach is based on the combination of the least squares approach with the spectral element method. The former frees the solution from spurious modes, that can be found sometimes in classical finite element simulations. Many examples of such non‐physical solutions exist in literature, and elimination of these spurious effects is a subject of great interest. Spectral elements are a numerical technique for solving partial differential equations which can be regarded as an extension of finite elements: they merge the flexibility of finite elements in dealing with complex geometries, and the better accuracy of spectral methods. Convergence to exact solution is improved by increasing (at run time) the polynomial degree, with no changes on the computational grid: this provides a significant advantage in respect to low order finite element, which necessarily have to resort to grid refinement. In the authors opinion this approach can be successfully used for the treatment of large scale electromagnetic problems or, alternatively, for applications where higher precision is required. We present a few numerical experiments which prove the capability of the method in object. Copyright © 2004 John Wiley & Sons, Ltd.     

A dual‐primal finite‐element tearing and interconnecting method combined with tree‐cotree splitting for modeling electromechanical devices

The dual‐primal finite‐element tearing and interconnecting (FETI‐DP) method is combined with the tree‐cotree splitting (TCS) method to expand the capability and improve the efficiency of the finite‐element analysis of electromechanical devices. With the FETI‐DP method, an original large‐scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. The TCS method is adopted to deal with the low‐frequency breakdown problem, which often accompanies the finite‐element analysis of electromechanical problems. On the basis of the computed magnetic field values, the force is computed with the use of the Maxwell stress tensor method. The proposed technique is applied to solve both high‐contrast magnetostatic problems and eddy‐current problems. Results are compared with both measurement data and brute‐force finite‐element calculations without domain decomposition. Comprehensive tests are conducted to investigate the parallel efficiency and numerical scalability. The results show that the proposed method can achieve a good parallel efficiency and an excellent numerical scalability with respect to the number of subdomains and the size of the problem. Copyright © 2012 John Wiley & Sons, Ltd.     

A one-step finite element formulation for the modeling of singleand double-circuit transmission lines

A method is presented, by which a finite element method (FEM) formulation is used for the direct computation of overhead transmission line series and sequence impedances. The method is applied in single and double circuit line configurations of arbitrary geometry, giving results in perfect agreement with those available from classical calculation methods. The new method can easily handle cases of nonhomogenous and/or irregular terrain, where classical methods may fail     

转子有辅助槽的表贴式永磁电机解析法建模与优化

通过在表贴式永磁电机的的转子上开辅助槽,可间接改善电机的齿槽转矩脉动状况.但目前相关文献大都基于有限元法,需要反复修改模型参数,且尚未得出明确的槽型优化方法.本文选取磁场中的标量磁位为求解变量,在电机的气隙区域、永磁体区域分别建立拉普拉斯和准泊松方程.对于不规则的永磁体形状,采用分块累加方法,提出了一种转子含有半圆形辅...     

A note on the thermal modelling of power semiconductor devices using the network analogue

The aim of this note is to point out that the boundary condition for the network modelling of thermal problems may have been incorrectly used in some previous studies. It is shown that the accuracy of the network analogue or the equivalent finite‐difference method is on the par with the finite‐element method for very fast transient thermal simulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Time domain global modelling of EM propagation in semiconductor using irregular grids

A two‐dimensional finite volume time domain (FVTD) method using a triangular grid is applied to the analysis of electromagnetic wave propagation in a semiconductor. Maxwell's equations form the basis of all electromagnetic phenomena in semiconductors and the drift‐diffusion model is employed to simulate charge transport phenomena in the semiconductor. The FVTD technique is employed to solve Maxwell's equations on an irregular grid and the finite box method is implemented on the same grid to solve the drift‐diffusion model for carrier concentration. The locations of unknowns have been chosen to allow linking coupled Maxwell's equations and transport equations in a seamless way. To achieve suitable accuracy and computational efficiency, using irregular grid topology allows a finer mesh in doped region and at junction, and a coarser mesh in substrate and insulting regions. The proposed scheme has been implemented and verified by characterizing electromagnetic wave propagation at microwave frequency in a semiconductor slab with arbitrary doping profile. Copyright © 2002 John Wiley & Sons, Ltd.     

Proposal for a benchmark model of a laminated iron core and a large‐scale and highly accurate magnetic analysis

This paper describes a benchmark model proposed for the clarification of the characteristic of various methods for modeling the laminated iron core. In order to obtain a reference solution of the benchmark model, a large‐scale nonlinear magnetostatic field analysis with a mesh fine enough to represent the microscopic structure of the laminated iron core is carried out by using the hybrid finite element–boundary element (FE‐BE) method combined with the fast multipole method (FMM) based on diagonal forms for translation operators. The computational costs and accuracy of two kinds of homogenization methods are discussed, comparing them with the reference solution. As a consequence, it is verified that the homogenization methods can analyze magnetic fields in laminated iron core within acceptable computational costs. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(1): 26–35, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20809     

Fourth‐order hybrid implicit and explicit‐FDTD method

A fourth‐order hybrid implicit and explicit finite‐difference time‐domain Method has been presented in this paper. This new method investigates the use of a second‐order accurate in time and a fourth‐order accurate in space. The 2D formulation of the method is presented and the time stability condition of the method is certified. The maximum time step size in this method is only determined by one spatial discretization. The numerical dispersion is discussed. Numerical examples demonstrate that when this method is used to solve electromagnetic problems, higher computational efficiency and less dispersion error can be obtained by comparing with the traditional finite‐difference time‐domain algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Development of Control Method for Outer‐Rotor Spherical Actuator

Conventional multi‐degree‐of‐freedom drive systems need many single‐degree‐of‐freedom actuators, but this makes the structure larger and heavier. The development of a spherical actuator should reduce the number of actuators, but the low torque and narrow rotation range are still problems. We developed a 2‐degree‐of‐freedom spherical actuator with an outer rotor that can produce a higher torque and wider rotation angle. In this paper, we propose a control method; we confirmed its usefulness by performing dynamic analysis using the three‐dimensional finite element method and by taking measurements with a prototype.