Open boundary eddy-current problems using edge elements (original) (raw)
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Approximate boundary element formulation for high-frequency eddy current problem
IEEE Transactions on Magnetics, 1993
This paper presents an approximate boundary element formulation for the high-frequency eddy current problem. The eddy currents are assumed to be surface currents at high-frequency induction, and the eddy current terms are treated using surface integration. In particular, we discuss the approximation of motional eddy current. The method presented is applied to a simple axisymmetric electromagnetic levitation problem. It is shown that our method is applicable to highfrequency induction problems. The advantage of this method is that the dimension of the system equations is considerably reduced in comparison with the usual boundary element analysis for these problems. That is, this method can be used with a comparative large element width. and has been engaged in improving computational electromagnetic engineering, the optimal design method by using the boundary element method, and research work on the electrical machine. ,
Nodal and Edge Finite Element Analysis of Eddy Current Field Problems
Przegląd Elektrotechniczny, 2008
Eddy current field problems can be solved by different potential formulations based on the "quasi-static" Maxwell's equations. The potential formulations are obtained using a vector potential and a scalar potential, the most widely used techniques are the A,V-A, the T,Φ-Φ formulations and their combinations. Vector potentials can be approximated by nodal or edge finite elements, scalar potentials are approximated by scalar elements. The paper presents and compares these formulations through TEAM Problem No. 7 containing a multiply connected region. Streszczenie. Problemy związane w prądami wirowymi mogą byc rozwiązywane przy wykorzystaniu roznych sformulowan i roznych potencjalow, bazujących na quasistatycznych rownaniach Maxwella. Wykorzystywany jet w tych sformulowaniach potencjal wektorowy i potencjal skalarny, najcześciej są to sformulowania A,V-A, oraz T,Φ-Φ, a takze ich kombinacje. Potencjal wektorowy jest aproksymowany przez elementy wezlowe i krawedziowe, a pot...
Characteristic impedance boundary conditions for the solution of open boundary problems
IEEE Transactions on Magnetics, 1993
Open boundary conditions are presented to solve partial differential equations by means of the finite element method. Characteristic impedance boundary conditions (CIBC) are imposed on an artificial boundary to match the external domain with the internal one, avoiding the reflections of the electromagnetic field. An alternative method based on the application of the Green's theorem is presented for lowfrequency fields since the electric and magnetic fields can be considered uncoupled. Mauro ."'eliziani received the Degree in E University of Rome "La Sapienza" in 1983. F been W O I king at the Department of Electric Engineen Electrical Engineering. At present he is As Electromagnetic Compatibility at the University of
IEEE Transactions on Magnetics, 2000
Since the magnetic permeability of steel is comparatively high, the skin depth may be a few millimeters even at a low frequency such as 50 Hz. And so, the impedance boundary condition (IBC) works effectively in most of the eddy current analyses. However the IBC is originally defined on the basis that the material property is linear, and so, in order to apply the IBC to nonlinear materials, we introduce a nonlinear IBC. With the help of the nonlinear IBC, we lessen the unknowns of the integral equations to give the boundary value to one and derive an integral equation with a loop current as the state variable. In order to check the adequacy and effectiveness of the proposed approach, we solve a typical eddy current problem while comparing computed results by the full equations and FEM.
Generating Source Field Functions With Limited Support for Edge Finite-Element Eddy Current Analysis
IEEE Transactions on Magnetics, 2000
A simple method is presented to generate impressed current vector potential functions with limited support whose curl yields a given net current. They are advantageously used in finite-element eddy current analysis employing a current vector potential represented by edge basis functions. A current vector potential describing a static current field with the given net current in the eddy current domain is first constructed. This source field is nonzero in the entire problem domain. Thereupon, it is restricted to a minimal simply connected region. The method is illustrated by a numerical example.
Numerical solution of eddy current problems in bounded domains using realistic boundary conditions
The aim of this paper is to analyze a finite element method to solve the low-frequency harmonic Maxwell equations in a bounded domain containing conductors and dielectrics, and using realistic boundary conditions in that they can be easily measured. These equations provide a model for the so-called eddy currents. The problem is formulated in terms of the magnetic field. This formulation is discretized by using Nédélec edge finite elements on a tetrahedral mesh. Error estimates are easily obtained when the curl-free condition is imposed explicitly on the elements in the dielectric domain.
IEEE Transactions on Magnetics, 2000
Surface impedance boundary conditions (SIBCs) are used for analysis of a wide range of practical applications such as micro strips, transformers or electrical machines. In this work the SIBC was implemented with classical edge elements using the magnetic vector potential. As known, the SIBC is afflicted with errors when it is being used on curved surfaces and near corners and edges. For this reason this paper investigates the error of the SIBC on curved surfaces. Therefore, simulations have been carried out for different radii and frequencies. The simulation results of the SIBC formulation have been compared with the common A 8 formulation for eddy current regions. It will be shown, that the error of the SIBC depends on the relation of the radius to the skin depth. Results are presented and discussed by means of a canonical problem.
IMA Journal of Numerical Analysis, 2012
The aim of this paper is to analyze a numerical method to solve transient eddy current problems with input current intensities as data, formulated in terms of the magnetic field in a bounded domain including conductors and dielectrics. To this end, we introduce a time-dependent weak formulation and prove its well-posedness. Under appropriate hypotheses on the input current intensities, we show that the weak solution has additional regularity and satisfies strong forms of the equations. We propose a finite element method for space discretization based on Nédélec edge elements on tetrahedral mesh, for which we prove well-posedness and error estimates. Furthermore, we introduce an implicit Euler scheme for time discretization and prove error estimates for the fully discrete problem. Moreover, a magnetic scalar potential is introduced to deal with the curl-free condition in the dielectric domain. This approach leads to an important saving in computational effort. Finally, the method is applied to solve two problems: a test with a known analytical solution and an application to electromagnetic forming.