Improved T−ψ nodal finite element schemes for eddy current problems

Kang, Tong; Chen, Tao; Zhang, Huai; Kim, Kwang Ik

doi:10.1016/j.amc.2011.05.062

Cited by 5 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the literature, we can find some papers related to the numerical analysis of the three-dimensional timedependent eddy current model in bounded domains containing conducting and dielectric materials [1,5,11,19,20,24]. Most of these articles deal with the case where the conducting materials are strictly contained in the computational domain and the source current is imposed in an inner subdomain.…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…However, when the conductors are multiply connected, the potential 1jJ may not be unique in the nonconductive region [8], and some special procedures need to ensure the 1jJ unique. In [5], a new T -1jJ finite element decoupled scheme only for the simply connected eddy current problem has been developed, which makes further reduction of computational cost and avoids saddle-point equations system. The aim of this paper is to extend the T -1jJ decoupled scheme with Crank-Nicholson difference format to solve the multiply connected eddy current problem.…”

Section: T-1jj Formulationmentioning

confidence: 99%

“…The coupled scheme (21)-(22) has been discussed in [5]. We alter the indices of time of the second term in the second formulation of (22) to obtain a novel discrete decoupled scheme for (15) as follows:…”

Section: T-1jj Formulationmentioning

confidence: 99%

A T-ψ decoupled scheme with C-N difference for a multiply connected eddy current problem

Chen

Wang

et al. 2012

Isape2012

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to present a new T-?jJ finite element decoupled scheme with Crank-Nicholson difference format for time-dependent eddy current problem, which avoids solving a saddle-point equations system and is more economical than the traditional scheme. The holes of multiply connected conductors are stemmed by making "cuts" and jumps of the function value ?jJ across the "cuts" are enforced. The construction of the finite element space with discontinuities at the "cuts" are given. The superior performance of the decoupled scheme is demonstrated by numerical experiment of the benchmark problem-TEAM Workshop Problem 7.

show abstract

“…In this framework, we refer to Alonso Rodrígiez , where the authors give a scalar potential‐based approach to eddy current problems. Several papers devote to numerical analysis of this method . The employment of the magnetic scalar potential ψ in nonconductive domain instead of the magnetic vector potential A in the A ‐ ϕ formulation brings a substantial reduction of computational cost by decreasing the degrees of freedom per node from three to one.…”

Section: Introductionmentioning

confidence: 99%

“…The employment of the magnetic scalar potential ψ in nonconductive domain instead of the magnetic vector potential A in the A ‐ ϕ formulation brings a substantial reduction of computational cost by decreasing the degrees of freedom per node from three to one. In , a new T ‐ ψ finite element decoupled scheme only for eddy current problem with a simply connected conductor has been developed. However, some problems arise when the conductors are multiply‐connected; the potential ψ e may not be unique in the nonconductive region , where we denote the scalar magnetic potential outside the conductors as ψ e to differentiate from ψ in the simply connected case.…”

Section: Introductionmentioning

confidence: 99%

A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Chen

Kang

et al. 2013

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

Communicated by M. CostabelThe aim of this paper is to develop a fully discrete .T, /-e finite element decoupled scheme to solve time-dependent eddy current problems with multiply-connected conductors. By making 'cuts' and setting jumps of e across the cuts in nonconductive domain, the uniqueness of e is guaranteed. Distinguished from the traditional T-method, our decoupled scheme solves the potentials T and -e separately in two different simple equation systems, which avoids solving a saddle-point equation system and leads to a remarkable reduction in computational efforts. The energy-norm error estimate of the fully discrete decoupled scheme is provided. Finally, the scheme is applied to solve two benchmark problems-TEAM Workshop Problems 7 and IEEJ model.

show abstract

Improved T−ψ nodal finite element schemes for eddy current problems

Cited by 5 publications

References 6 publications

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

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

A T-ψ decoupled scheme with C-N difference for a multiply connected eddy current problem

A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Contact Info

Product

Resources

About

Improved T−ψ nodal finite element schemes for eddy current problems

Cited by 5 publications

References 6 publications

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

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

A T-&#x03C8; decoupled scheme with C-N difference for a multiply connected eddy current problem

A (T,ψ)‐ψe decoupled scheme for a time‐dependent multiply‐connected eddy current problem

Contact Info

Product

Resources

About

A T-ψ decoupled scheme with C-N difference for a multiply connected eddy current problem

A (T,ψ)‐ψ_e decoupled scheme for a time‐dependent multiply‐connected eddy current problem