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Title: FINITE ELEMENTS IN ELECTROMAGNETICS: A JUBILEE REVIEW
Abstract: This review describes the historical origins and the present state of the finite element method in electromagnetics. The foundation principles of finite elements are briefly reviewed. Applications are mainly to two and three dimensional problems of microwave and optical structures. The major types of scalar element are noted, and edge-interpolative vector elements are reviewed, firstly for the waveguide problem and then in three dimensions. An extensive bibliography is given, particularly stressing review papers. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 10-24]
Author(s): J. Brian Davies, Peter P. Silvester
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: COMPATIBILITY RELATIONS FOR TIME-DOMAIN AND STATIC ELECTROMAGNETIC FIELD PROBLEMS
Abstract: When computing an electromagnetic field using a numerical method, e.g. the finite element method, it is possible that, although Maxwell's equations are discretized accurately, highly inaccurate computational results are obtained. In those cases it can easily be shown that (some of) the electromagnetic compatibility relations (field properties that follow from Maxwell's equations) are not satisfied. The divergence condition on the fluxes, for instance, follows directly from the field equations but not necessarily from their discretized counterparts. This necessitates inclusion of the compatibility relations in the finite-element formulation of the field problem. First a survey is given of all electromagnetic compatibility relations for the time-domain electromagnetic field equations. Subsequently the compatibility relations for the static field equations are discussed. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 25-29]
Author(s): Ioan E. Lager, Gerrit Mur
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: THE APPLICATION OF THE FINITE ELEMENT METHOD IN DESIGN OF ELECTRIC MOTORS
Abstract: The classical approach to design of electric motors is based on the concept of simplified magnetic circuit analysis. This approach fails in today's design situation due to utilization of new materials and new designs. Application of sophisticated numerical methods becomes inevitable. Some problems arising in the application of the finite element method in design of electric motors are discussed in this paper. Electric motors are always part of a system and their behaviour within the system, which is characterized by integral parameters (torques and reactances), should be known at the design stage. Computation of these parameters from a finite element magnetic field solution is described here. The computation of torque/angle characteristics from finite element field solution by application of two basic approaches: - global virtual work method and cubic spline interpolation technique, - Maxwell stress tensor integration, is described. The applicability of both approaches is illustrated by computation of the torque in a switched reluctance motor and the advantages of virtual work approach are emphasised. The main problem in application of the finite element method to computation of magnetic fields in electric motors is that the field sources (currents) and load angle are unknown. External environment (terminal voltage and mechanical load) are known, and the magnetic field solution is iterated until the external constraints are satisfied. To avoid finite element mesh rotation an iterative process was implemented in which only the fundamental harmonic of the lumped stator winding distribution is taken into consideration instead of the three-phase winding excitation. The direct and quadrature reactances are computed from the finite element magnetic field solution utilizing flux linkage and stored energy approaches. The procedure is illustrated by computation of the reactances of a permanent magnet synchronous electric motor. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 30-36]
Author(s): Z. Haznadar, Z. Stih, S. Berberovic, G. Manenica
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: COMPUTATION OF STATIC AND QUASISTATIC ELECTROMAGNETIC FIELD USING ASYMPTOTIC BOUNDARY CONDITIONS
Abstract: This paper presents the computation of static and quasistatic electromagnetic fields using asymptotic boundary conditions (ABC). Asymptotic boundary conditions for eddy current problems due to external field excitations are derived. For electrostatic fields, ABC-s are used in conjunction with Laplace's equation while for quasistatic magnetic fields, ABC-s are employed in conjunction with the integrodifferential finit element method. The effect of outer boundary locations on the accuracy of the simulation results is examined. This study shows that in these cases, ABC-s can improve the computation accuracy compared to the usual truncation of outer boundaries. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 37-42]
Author(s): Qiushi Chen, Adalbert Konrad, Paul P. Biringer
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: THREE METHODS FOR EVALUATION OF FREQUENCY-DEPENDENT RESISTANCES AND INDUCTANCES OF MULTICONDUCTOR TRANSMISSION LINES
Abstract: Three methods for the analysis of frequency-dependent resistances and inductances of multiconductor transmission lines are outlined and compared. The first method comes from power-engineering applications, and it is based on a numerical solution of an integral equation for the distribution of the conductor volume currents. The second method is based on the perturbation technique. The third method comes from high-frequency applications, and it is based on the principle of equivalent surface electric and magnetic currents. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 43-56]
Author(s): Antonije R. Djordjevic, Tapan K. Sarkar
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: NUMERICAL SOLUTIONS OF WAVE PROPAGATION IN DISPERSIVE AND LOSSY TRANSMISSION LINES
Abstract: A numerical model is proposed for application to dispersive transmission lines. Numerical results are compared with the analytical solution of the dispersive wave equation based on the wave propagation solved by means of finite element method in one dimension case and Newmark- method in the time domain. This comparison between numerical and analytical solutions validates this numerical method as a suitable method to study wave propagation in dispersive transmission lines. Several practical applications including electromagnetic propagation in a plasma and the transient response of a surge wave in high-voltage transformer windings are presented in this paper. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 57-66]
Author(s): Junwei Lu, Yukio Kagawa, David V. Thiel
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: EQUIVALENT ELECTRIC CIRCUITS APPROACH FOR THE MODELING OF NON-LINEAR ELECTROMAGNETIC FIELDS
Abstract: In this paper a method for the analysis of non-linear three dimensional electromagnetic field is presented The conductive and magnetic regions of the examined system are subdivided in elementary volume elements in which a uniform current density J and magnetization M is assumed. By integrating Ohm's law inside the conductive regions, a set of equations representing the equilibrium equations of an equivalent electric network is obtained. The knowledge of the currents in the conductive regions allows the evaluation of the electromagnetic fields and the determination of the forces among different bodies. Applications of the method to the solution of benchmark problems of time varying linear systems, and non-linear static cases are presented. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 67-73]
Author(s): M. Gimignani, A. Musolino, M. Raugi, A. Tellini
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: AN IMPROVED NETWORK MODEL FOR EDDY CURRENT PROBLEMS
Abstract: This paper describes improvements in modelling Maxwell's equations in two dimensions using the electrical network analogue. Two network models are described with major emphasis placed on diffusion dominated problems. The first one is the combined fine-coarse mesh approach which was initially developed for the method of transmission-line modelling (TLM). The combined fine-coarse mesh technique is then modified by introducing controlled sources at the interfacing between the fine and the coarse mesh. Several numerical experiments, including one with both a conducting region and free space, are used to study the two models. They are also compared with the standard network analogue using a regular meshing. Numerical results are compared with analytical or published data. In all cases, SPICE (or PSPICE) has been used to solve the resulting network analogues. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 74-82]
Author(s): Chi-Chung Wong
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: ON THE USE OF PLANAR SCATTERING PROBLEM TECHNIQUES TO ANALYZE THIN PLANAR QUASI-MAGNETO-STATIC SHIELDING
Abstract: A metallic screen scattering technique developed for microwave and millimetre wave applications is adapted, using the principle of duality to a quasi-magnetostatic shielding problem. In the limiting case of low frequency (0.01 Hz) the results compare favourably with the static solution. Moreover, this adaptation is expanded to treat finite permeability shields. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 83-92]
Author(s): C.D. Hechtman, E.H. Lenzing, B.S. Perlman
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: THE FINITE DIFFERENCE METHOD IN MAGNETIC FIELD PROBLEMS
Abstract: Finite difference techniques are widely used in the solution of electromagnetic boundary value problems, but seldom employed with static or quasi-static field problems. Historically this departure was warranted by (1) the relative ease by which problem geometries can be modeled using the finit element counterpart, and (2) the lack of symmetrical properties and large banding in the governing matrices. Presented here are some methods for generalizing the finite difference approach so that problem definition is easily modeled and Hermitian matrices result. The technique uses a conventional finite difference grid placed in the work area irrespective of the problem geometry. Finite difference equations are written in their simplest form across the problem work space. Boundary conditions are then introduced after the bulk equations are in place. The problem is solved using a non square governing matrix in a least square sense. This is accomplished most easily by premultiplying the matrix equation by its transpose. An alternative to the preconditioned conjugate gradient technique for solving the resultant matrix equation is to seek the eigenvalues for the system and express the answer as a sum of the eigenvectors. Results are shown for a salient pole motor. The technique is very useful in handling rotating or translating problems where considerable attention must be given to the proper connection and re-connection of the grid points. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 93-97]
Author(s): Kent R. Davey
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: A CASE STUDY COMPARING THE LOSSY WAVE EQUATION TO THE CONTINUITY EQUATION IN MODELING LATE-TIME FIELDS ASSOCIATED WITH LIGHTNING
Abstract: An investigation is presented into lightning-related transient electric field and conduction current densities due to the redistribution of charge by the return stroke (late-time effects). A qualitative comparison is made between the late- time vertical electrical field magnitudes predicted by two solutions via the continuity equation/Poisson's equation and the continuity equation in conjunction with the lossy wave equation. The differences between these results indicate that the magnetic energy density created by a lightning discharge generally provides relevant changes in the resulting electrical field waveforms as radial and vertical distances increase from the lightning discharge. That is, the accuracy of the conservative field assumption x E = 0 decreases with the distance from the point of excitation to the point of observation of the electric field for the study conducted. This observation suggests the use of the lossy full wave equation, when computationally feasible, for the prediction of late-time electric field behavior. This study addresses trends in the general behavior of the two solutions over region 0 <= r <= 30 km and 30 <= z <= 50 km. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 98-110]
Author(s): Micheal E. Baginski, A. Scottedward Hodel
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: APPLICATION OF BEM FOR CALCULATING THE PARAMETERS OF CABLES AND TRANSMISSION LINES
Abstract: The capacitances of three phases cable and the characteristic impedance of coaxal transmission line with complicated shape of the cross sections are evaluated by using boundary element method. The calculated results obtained by the proposed method are coincident well with the results given by the literatures [2-9]. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 111-113]
Author(s): Zhou Pei-bai, Zhong Hon-yu
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: HIGH FREQUENCY FFT ANALYSIS OF AN ELECTRICALLY LONG MONOPOLE ANTENNA
Abstract: In previous work the currents along a monopole, 20 meters long and operating at 299.8 MHz, placed over a perfectly conducting ground plane were analyzed using several modeling techniques and the Numerical Electromagnetics Code version two (NEC-2). An interesting topic to investigate is the presence of spurious modes of propagation along the monopole. Such modes of propagation are studied for each modeling technique, and conclusions are drawn accordingly. When the data are transformed into the k- space domain, using Fast Fourier Transforms (FFT), the spurious mode behavior along the monopole becomes clearly visible. This technique provides valuable information not yet documented. [Vol. 9, No. 2 (1994), pp 114-119]
Author(s): Saad N. Tabet
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: RESPONSE OF EXTERNALLY EXCITED COAXIAL CABLES WITH WIRE BRAIDED SHIELDS
Abstract: The frequency responses of coaxial cables employing wire braided shields, excited by external fields is studied using an algorithm based on distributed circuit model, which uses both electric and magnetic field parameters to model the external field coupling. Simplicity and fast speed of the model enable computer aided analysis of externally induced noise in cable interconnects to be carried out in a computationally efficient manner. A general CAD algorithm is developed based on this model and it is applied to study the response of cables over a lossless ground plane. The algorithm is then used to study the effects of different braid constructions on the responses of cables excited by external fields. Responses of cables with optimum braid designs in their shields are studied in detail. The model uses the experimental values of the leakage parameters which are measured separately using a standard triaxial text fixture. [Vol. 9 No. 2 (1994), pp 120-126]
Author(s): S. Sali
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: HIGH SPATIAL RESOLUTION ANALYSIS OF ELECTRIC CURRENTS INDUCED IN MAN BY ELF MAGNETIC FIELDS
Abstract: This paper presents the formulation of the impedance network method that allows computation of the arbitrary injection currents on the boundary of a selected sub-region for an analysis of induced electric current distributions inside the human body exposed to extremely low frequency magnetic fields. The obtained formulation provides a high resolution modeling of a local region of interest without using an excessively large number of computational cells. The iterative equations for outer and inner nodes are derived in detail. Solutions for a double-layered sphere are then calculated to verify the derived equations. The errors involved in the calculation are also examined. To illustrate the method, its application to computations of the induced currents in the human head is described. [Vol. 9, No. 2 (1994), pp 127-134]
Author(s): Weiguo Xi, Maria A. Stuchly
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: A VECTORIZED MULTIPLE PLATE SCATTERING CODE
Abstract: A computer code named Vectorized Multiple Plate Scattering (VMPS) code has been developed at the Ohio State University ElectroScience Laboratory to compute the scattered fields from structures that can be modelled using perfectly conducting flat plates. The VMPS code uses a moment method approach to solve an electric field integral equation for the scattered fields. The code utilizes the vectorization capability of CRAY supercomputers to compute the scattered fields very efficiently. In this paper, the operation of the VMPS code is described and its vectorization efficiency is demonstrated. [Vol. 9, No. 2 (1994), pp 135-141]
Author(s): John W. Nehrbass, Inder J. Gupta
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: PARTIAL SURVEY OF CODES FOR HIGH FREQUENCY SCATTERING FROM FACET MODELS OF RADAR TARGETS
Abstract: In this work, four high-frequency electromagnetic scattering codes are surveyed with regard to their capabilities and limitations for the calculation of the radar cross section (RCS) of facet models of targets. The codes discussed are MISCAT, NRCPTD, McPTD, and Xpatch. All of these codes utilize the physical theory of diffraction (PTD) to approximate the field scattered from the target. A short discussion of the modeling features of each code is given and some sample numerical results are generated. It is concluded that, of the models considered here, Xpatch possesses the most comprehensive modeling features available, with no loss in accuracy over the other codes. [Vol. 9, No. 2 (1994), pp 142-153]
Author(s): Michael A. Richards
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: AN EXPERIMENTAL AND THEORETICAL INVESTIGATION OF SCATTERING BY FINITE PERFECTLY CONDUCTING CYLINDERS WITH VARYING CROSS-SECTION
Abstract: In this paper we consider the problem of scattering from a class of three dimensional (3-D) targets which are finite cylinders but whose cross-section varies along the axis of the structure. We devise a technique wherein the solution to this 3-D problem is reduced to a sequency of two dimensional (2-D) problems. Solutions of 2-D problems are easier to obtain than the solutions of 3-D problems and further a variety of well established 2-D methods are available. This procedure results in a dramatic reduction in computational complexity and also makes the technique suitable for implementation on computers with highly parallel architectures. A number of targets with ogival and elliptical cross-sections were built and their back-scattered RCS was measured at 3, 6 and 10 GHz. Good agreement between computed and experimental results is obtained validating the technique described here. [Vol. 9, No. 2 (1994), pp. 154-161]
Author(s): Krishna M. Pasala, Carlos R. Ortiz
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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Title: AUTOMATIC AND EFFICIENT SURFACE FDTD MESH GENERATION FOR ANALYSIS OF EM SCATTERING AND RADIATION
Abstract: The finite difference time domain (FDTD) method has found very wide applications in the analysis of electromagnetic scattering and radiation. The first and most important issue of the FDTD modeling is to decompose a computation space, containing a given geometry, into FDTD unit cells. There are a few dedicated mesh generators which could discretize the space into cells for general analysis. However, among FDTD applications, a large portion of them deal with objects structured primarily with conducting and/or thin-dielectric plates, such as a conducting sphere or cube, a cavity, an airplane, etc. The mesh data necessary to input are those of node indices and material parameters on the object surface. Consequently geometry modeling is essentially to generate FDTD cells on the surfaces. For this purpose, a simple and effective algorithm capable of on- surface FDTD mesh generation is introduced based on a ray-tracing method. The algorithm presumes that the input geometry is described in polygons and lines which are often approximations of smooth surfaces and thin wires. In output, the algorithm decomposes automatically the polygons and lines into on-surface cells compatible with, and readable by, an FDTD solver. The algorithm has been coded in programs allowing effective and automatic generation of surface cells on various high- or low-end computer platforms. [Vol. 9, No. 2 (1994), pp 162-169]
Author(s): W. Sun, M.P. Purchine, J. Peng, C.A. Balanis, G.C. Barber
File Type: Journal Paper
Issue:Volume: 9      Number: 2      Year: 1994
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