A posteriori error estimator for harmonic A‐φ formulation

Tang, Zuqi; Menach, Yvonnick Le; Creusé, Emmanuel; Nicaise, Serge; Piriou, F.; Nemitz, Nicolas

doi:10.1108/03321641311317040

Cited by 5 publications

(11 citation statements)

References 11 publications

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“…As the voltage V is known here, we obtain a similar system to the one discussed in [7]. Second, if we impose the current I , the voltage V is unknown, and with the imposed current intensity I through the electric port as defined in (4), the definition of α, and an integration by parts, we obtain a supplementary integral equation…”

Section: A A/ϕ Formulationmentioning

confidence: 99%

“…The equations of time-harmonic eddy current problems take the following form: where E is the electric field, B is the magnetic flux density, H is the magnetic field, J ec is the eddy currents, J s is a given divergence-free applied current density, ω is the pulsation, μ is the magnetic permeability, and σ is the electrical conductivity. In [6] and [7], the conductor domain D c was assumed to be strictly included in the domain D, so that the only source term was the given current density J s . In general, if the geometry is symmetric, the computation can be reduced to only one part of it.…”

Section: Numerical Modelmentioning

confidence: 99%

“…ERROR ESTIMATOR In [6] and [7], residual-based a posteriori error estimators are derived for the harmonic A/ϕ and T/ formulations in the case where the source term only consists in imposing a current density J s and where the boundary conditions correspond to B.n = 0. Our estimators are based on the verification of the equation in each element, the evaluation of all weakly verified quantities by each formulation, and the boundary conditions.…”

Section: B T/ Formulationmentioning

confidence: 99%

“…In the following, we will present our estimators, which verify the two properties: 1) reliability; and 2) efficiency, which have been introduced in [6] and [7].…”

Section: B T/ Formulationmentioning

confidence: 99%

“…Their reliability and efficiency have been mathematically proven and their performances have been well evaluated on various examples (see [2] for electric field formulation, and [6] and [7] for potential formulations). In [6] and [7], residual-based estimators are presented in detail, but with some constraints on the boundary conditions and source terms. In this paper, we extend the previous results to the general case with different source terms for both A/ϕ and T/ potential formulations of eddy current problems.…”

Section: Introductionmentioning

confidence: 99%

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Residual <italic>a Posteriori</italic> Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

et al. 2015

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In the modeling of eddy current problems, potential formulations are widely used in recent days. In this paper, the results of residual-based a posteriori error estimators, which evaluate the discretization error in the finite-element computation, are extended to the case of several kinds of source terms for both A/ϕ and T/ harmonic formulations. The definitions of the estimators are given and some numerical examples are provided to show the behavior of the estimators.Index Terms-A posterior error estimator, eddy current problem, potential formulation, source terms.

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Section: A A/ϕ Formulationmentioning

confidence: 99%

Section: Numerical Modelmentioning

confidence: 99%

Section: B T/ Formulationmentioning

confidence: 99%

“…In the following, we will present our estimators, which verify the two properties: 1) reliability; and 2) efficiency, which have been introduced in [6] and [7].…”

Section: B T/ Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Residual <italic>a Posteriori</italic> Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

et al. 2015

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Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems

Creusé,

Nicaise,

Tang

2024

IMA Journal of Numerical Analysis

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In this work, we propose an a posteriori goal-oriented error estimator for the harmonic $\textbf {A}$-$\varphi $ formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of an adjoint problem associated with the initial one. For each of these two problems, a guaranteed equilibrated estimator is developed using some flux reconstructions. These fluxes also allow to obtain a goal-oriented error estimator that is fully computable and can be split in a principal part and a remainder one. Our theoretical results are illustrated by numerical experiments.

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A posterioriresidual error estimators with mixed boundary conditions for quasi-static electromagnetic problems

Tang

Menach

Creusé

et al. 2015

COMPEL

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Purpose -The purpose of this paper is to propose some a posteriori residual error estimators (REEs) to evaluate the accuracy of the finite element method for quasi-static electromagnetic problems with mixed boundary conditions. Both classical magnetodynamic A-φ and T-Ω formulations in harmonic case are analysed. As an example of application the estimated error maps of an electromagnetic system are studied. At last, a remeshing process is done according to the estimated error maps. Design/methodology/approach -The paper proposes to analyze the efficiency of numerical REEs in the case of magnetodynamic harmonic formulations. The deal is to determine the areas where it is necessary to improve the mesh. Moreover the error estimators are applied for structures with mixed boundary conditions. Findings -The studied application shows the possibilities of the residual error estimators in the case of electromagnetic structures. The comparison of the remeshed show the improvement of the obtained solution when the authors compare with a reference one.Research limitations/implications -The paper provides some interesting results in the case of magnetodynamic harmonic formulations in terms of potentials. Both classical formulations are studied. Practical implications -The paper provides some informations to develop the proposed formulations in the software using finite element method. Social implications -The paper deals with the possibility to improve the determination of the meshes in the analysis of electromagnetic structure with the finite element method. The proposed method can be a good solution to obtain an optimal mesh for a given numerical error. Originality/value -The paper proposes some elements of solution for the numerical analysis of electromagnetic structures. More particularly the results can be used to determine the good meshes of the finite element method.

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A posteriori error estimator for harmonic A‐φ formulation

Cited by 5 publications

References 11 publications

Residual <italic>a Posteriori</italic> Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

Residual <italic>a Posteriori</italic> Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems

A posterioriresidual error estimators with mixed boundary conditions for quasi-static electromagnetic problems

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