A parametric convex meshfree formulation for approximating the Helmholtz solution in circular coaxial waveguide

The application of convex meshfree approximation to the time‐harmonic electromagnetic wave propagation analysis of a waveguide with non‐convex cross section such as the circular coaxial waveguide remains unsolved. This paper introduces a parametric convex meshfree formulation for the circular coaxial waveguide analysis. The present method reformulates the convex meshfree approximation on the basis of a special parametric space―an extended parametric domain. The new parametric domain ensures a one‐to‐one geometric mapping using the convex meshfree approximation and allows the convex meshfree method to be applied to the oscillatory type of Helmholtz equation for circular coaxial waveguide analysis. Both transverse electric and transverse magnetic mode studies are conducted using the present method, and results are compared with the standard bilinear finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

薄壳单元法在接触物体间电磁力计算中的应用

针对在利用有限元法计算接触物体间电磁力时在物体接触表面没有积分单元可用的问题,首先,基于薄壳单元的思想,提出了一种在体积分和面积分之间确定附加薄壳单元的方法和一种在3D有限无法中利用附加薄壳单元精确计算接触物体间电磁力的方法,然后,基于虚功原理,推导了计算薄壳单元节点电磁力的T-Ω公式和雅可比矩阵表达式,并给出了计算物体接触表面分布电磁力的算法及其实现方法,最后将所提出的方法用于实例计算,并将3D有限元法计算结果与解析计算结果进行比较,证实所提出方法的有效性和正确性.     

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.     

A conformal mapping‐based approach for fast two‐dimensional FEM electrostatic analysis of MEMS devices

In this paper, a methodology is proposed for expediting the coupled electro‐mechanical two‐dimensional finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by mapping the deformed electrostatic domain to the reference undeformed domain ‘conformally’. A ‘conformal’ map preserves the form of the Laplace equation and the boundary conditions; thus the electrostatic problem is solved only once in the undeformed electrostatic domain. The conformal map itself is generated through the solution of the same Laplace equation on the undeformed geometry and with displacement boundary conditions dictated by the movement of the mechanical domain. The proposed methodology is demonstrated through its application to the modeling of three MEMS devices with varying length‐to‐gap ratios, multiple dielectrics and complicated geometries. The accuracy of the proposed methodology is confirmed through comparisons of its results with results obtained using the conventional finite element solution. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite element method investigation of electrostatic precipitator performance

This paper aims at analysis of the monopolar ionized field in electrostatic precipitator. A numerical model for simulating precipitation of particles in electrostatic precipitator is discussed in this paper. It includes all essential phenomena affecting the process. An iterative finite‐element technique is used to solve Poison's equation. We proposed the introduction of a potential corresponding to the critical minimum ionization field directly in the finite element formulation as a Dirichlet condition. The theoretical migration velocity is obtained by balancing the drag force with the Coulomb force or electrostatic force acting on a particle. We used the model introduced by Cochet for predicting a particle charge. The model assumes that a particle of the same size attains an equivalent maximum amount of charge for a charging time equal to infinity. Particles influence the electrical field, flow field, electrical migration velocity, gas discharge, particle charge and collection efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

A characteristics-based finite element method for transmission line problem

This paper presents a numerical model of transmission line equations based on a combination of the finite element method and the generalized method of characteristics. A local system of the transmission line finite element is obtained using the generalized method of characteristics applied to the Telegrapher's equations. In this way, a spatial functional approximation using local shape functions together with the generalized trapezoidal rule used for time integration as it is done in the classical finite element formulation is avoided and higher accuracy of results is obtained. In order to show the essential principles of the proposed numerical method, for sake of simplicity, the scope of the paper is restricted to a single transmission line problem at the low frequency regime.     

Element‐free Galerkin method to the interface problems with application in electrostatic

The purpose of this paper is to develop the element‐free Galerkin method for a numerical simulation of the second‐order elliptic equation with discontinuous coefficients. Discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. The proposed method is one of the powerful meshless methods based on moving least squares approximation. The element‐free Galerkin method uses only a set of nodal points to discretize the governing equation. No mesh in the classical sense is needed, but a background mesh is used for integration purpose. A quadrilateral mesh unfitted with the interface is used for integration objective. The Lagrange multipliers are used to enforce both Dirichlet boundary condition and Dirichlet jump condition. The presented numerical experiments confirm the efficiency of the proposed method in comparison with some existing methods for interface problems. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

A 3D finite element analysis of large‐scale nonlinear dynamic electromagnetic problems by harmonic balancing and domain decomposition

The dual–primal finite element tearing and interconnecting (FETI‐DP) method is applied together with the harmonic balance method and the fixed‐point (FP) method to improve the efficiency of three‐dimensional finite element analysis of large‐scale nonlinear dynamic electromagnetic problems. The FETI‐DP method decomposes the original problem into smaller subdomains problems. Combined with parallel computing techniques, the total computation time can be reduced significantly. To account for nonlinear B‐H characteristics, the FP method is applied together with the polarization formulation. Because the FP method assumes a constant reluctivity, it decouples the systems of different harmonics. The FETI‐DP method can then be applied to speed up the simulation of each harmonic in each FP iteration. Two benchmark problems and a three‐phase inductor are simulated by the proposed method to validate the formulation and demonstrate its performance. Copyright © 2015 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     

Modeling the pull‐in behavior of electrostatically actuated micro beams by an approximate finite element method

We establish the deflection functions of electrostatically actuated micro beams by an approximate finite element method (AFEM), in which the beam and the electrostatic load are discretized. The beam is replaced with a series of beam elements by traditional FEM. Using the total differential of the distributed electrostatic force, we represent such a force with the nodal forces on the beam elements. We calculate the deformation curve of the beam by gradually loading voltage in small increments, and pull‐in behavior is identified when the convergence of the deflection iteration cannot be achieved after voltage increment. The proposed method considers the effect of deformation on stiffness by establishing a new equivalent stiffness matrix for each voltage step based on of the results of previous steps. Through this approach, we prevent the approximate errors of the stiffness matrix from accumulating. The AFEM results on micro beams with different geometries indicate good agreement with those obtained by other studies and those derived using commercial FE software. Copyright © 2013 John Wiley & Sons, Ltd.     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite element method solutions of field distributions in large cavities

To make possible the application of the three-dimensional finite element method to electrically large problems, it is combined with the analytical solutions of arbitrary large cavity with aperture. In this paper, detailed analysis for this hybrid method is presented. The element matrices necessary for coupling the finite element method to analytical solutions are given. The proposed hybrid method significantly reduces the number of unknown since only the inhomogeneity needs to be discretized. Thus computer memory and storage demands are reduced. In addition. This hybrid method employs the edge element which is not expected to produce spurious solutions. Also, the formulation presented in this paper preserves the sparsity of the finite element matrix, and does not require any matrix inversion. This new hybrid method is used to compute the field distributions in various partially filled rectangular enclosure. The results match well with the pure edgebased finite element method and analytical solutions.     

Nonlinear distortion analysis via perturbation method

An analytical method based on the classical perturbation method and the harmonic balance method is presented to analyze the distortion due to circuit nonlinearities. Starting from the time‐domain‐modified nodal analysis formulation for a nonlinear dynamic circuit, a calculation procedure of the periodic solution is developed, leading to general formulae for harmonics and nonlinear distortion figures. These formulae are then particularized for the widely used polynomial and exponential nonlinearities. Circuit simulations are performed showing the accuracy of the presented formulae. Copyright © 2009 John Wiley & Sons, Ltd.     

Efficient hybrid scheme of finite element method of lines for modelling computational electromagnetic problems

A hybrid scheme called finite element method of lines is proposed and described for modelling and analysis of generalized computational electromagnetic problems with emphasis on a number of irregular waveguide examples. This new technique is developed by combining a finite element method with a method of lines so that it can handle not only irregular composite geometry but also maintain high accuracy enjoyed by semi‐analytical procedures. Analytical and numerical algorithmic building blocks of this new scheme are discussed in detail such as geometry discretization, element mapping, element trial functions, reformulation and computational issues of non‐linear ordinary differential equations. Our results show that this new technique is able to efficiently solve complex problems as compared with the conventional method of lines. Copyright © 2004 John Wiley & Sons, Ltd.     

拱坝应力分析中的有限元内力法

本文提出了拱坝应力分析的有限元内力法，该法首先按常规方法建立拱坝及地基在水压力，自重等荷载作用下的有限元平衡方程，求解结点位移和单位应力，然后将坝体分解为拱系和梁系，根据拱和梁的内力平衡条件求解指定截面上的约束内力，并进而求解应截面上的内力（弯矩、轴力、剪力等）和坝体内任一点的等效应力。文中推导出了相应的计算公式，并通过对典型的圆筒拱坝和拟建的某高拱坝的应力分析说明了该方法的正确性。     

Monte Carlo simulation for stochastic calculus of far‐field radiation from open‐ended waveguide arrays

In this paper, Monte Carlo (MC) simulation has been applied for the analysis and stochastic calculus of far‐field radiation from the small, large, and infinite open‐ended waveguide arrays. Elements of the arrays are excited by the fundamental TE₁₀ mode and with equal amplitude and linear phase. The simulated results from MC are compared closely with the finite element method (FEM). Numerical analysis based on FEM is performed using Ansoft High Frequency Structural Simulator to calculate the far‐field radiation characteristics of the arrays. The accuracy and the effectiveness of the aforesaid method, which is based on Monte Carlo integration technique, are also demonstrated in uniformly and nonuniformly spaced waveguide arrays for pattern synthesis or achieving side lobe level reduction. The arrays with arbitrary shapes are simply evaluated by MC method in equal spacing array. It is found that by applying MC simulation, the open‐ended waveguide arrays have the ability to produce the desired radiation pattern and could satisfy requirements for many applications. Copyright © 2016 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.     

Numerical electric field analysis of capacitance and potential in space for estimation of permittivity distribution

We have been studying on measuring capacitance and potential using long‐distance electrode for estimating a permittivity distribution. The estimating method of permittivity distribution was proposed using finite element method (FEM) and genetic algorithm. However, the measurement accuracy was not reviewed. In this paper, we carried out numerical analysis using FEM in case of change of diameter, position, and permittivity of a rod of dielectric and discussed the measurement accuracy of capacitance and potential.