An optimal method for 3-D eddy currents

Emson, C.R.I.; Simkin, J.

doi:10.1109/tmag.1983.1062910

Cited by 142 publications

(40 citation statements)

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“…With this aim we introduce the following conditions as in [1,3] which assumes absence of electric charge in the dielectric domain: 12) where ǫ is the electric permittivity and g is an additional data. Notice that Γ 1…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The time primitive of the electric field has been introduced in the literature of electrical engineering in [12] and it is usually known as modified magnetic vector potential. This potential has been used later by other authors (see, for instance, [17,18,22]) which usually couple this vector field with different unknowns in the dielectric part.…”

Section: Introductionmentioning

confidence: 99%

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An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions

et al. 2013

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Abstract. The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space discretization based on Nédélec edge elements for the main variable and standard finite elements for the Lagrange multiplier, for which we obtain error estimates. Then, we introduce a backward Euler scheme for time discretization and prove error estimates for the fully discrete problem, too. Finally, the method is applied to solve a couple of test problems.Résumé. L'objectif de cet article est d'analyser une formulation du problème des courants de Foucault,écrite en fonction d'une primitive en temps du champélectrique, dans un domaine borné, et etant les intensités du courant ou les chutes de potentiel les sources données du problème.À ce propos, nous introduisons un multiplicateur de Lagrange pour imposer la condition de divergence nulle dans le domain diélectrique et nous obtenons une formulation faible mixte conduisantà un problème parabolique dégénéré, pour lequel l'existence et l'unicité d'une solution sont démontrées. Nous proposons une discretisation spatiale du problème, basée sur deséléments finis d'arête de Nédélec pour la variable principale et sur deséléments finis nodaux standard pour le multiplicateur de Lagrange. Nous obtenons des estimations d'erreur pour cette discrétisation. Nous introduisons ensuite un schéma d'Euler implicite pour la discretisation en temps et nous démontrons des estimations d'erreur por le problème complètement discretisé. Finalement, la méthode est appliquéeà la résolution de quelques problèmes test.1991 Mathematics Subject Classification. 65N30, 78A25.

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Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions

et al. 2013

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“…Emson and Simkin (1983), in the presented form, to our knowledge, a detailed mathematical analysis has not been conducted. Emson and Simkin discuss the uniqueness but take the existence of the solution for granted.…”

Section: Discussionmentioning

confidence: 99%

Vector potential formulation of a quasi-static EM induction problem: existence, uniqueness and stability of the weak solution

2011

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We deal with the electromagnetic induction in a conductor with 3D distribution of electric conductivity in quasi-static approximation with the focus on theoretical aspects related to the solvability of this problem. We formulate the initial, boundary-value problem of electromagnetic induction in terms of a magnetic vector potential only, first in differential and then in integral forms. We prove that the problem is well posed in the Hadamard sense, that a solution exists, is unique and continuously dependent on data. The fact that no electric scalar potential is employed in the formulation and no gauge condition is imposed on the magnetic vector potential makes the formulation attractive for numerical implementations.

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“…The methods except the A -@ method shown in Table 1 cannot be applicable to a model with holes, because the magnetic scalar potential 9 cannot be defined in the region where the interlinkage of currents exists [3]. Though two kinds of modeling methods as shown in Fig.1 have been proposed[6] to overcome t h i s difficully, the method shown in Fig.l(a) is not Table 1.…”

Section: Modeling Of Holesmentioning

confidence: 99%

“…The A*-R and E -Q methods are preferable from the viewpoints of the computer storage and the CPU time. A-@-S2 [2], A * -Q [3], T -Q L.41 and E -R [ 5 ] methods, have been proposed for 3-D eddy current analysis, the advantages and disadvantages of each method are not discussed systematically until now. It is important to know the most preferable (accurate and fast) method in order to solve a given problem.…”

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confidence: 99%