Finite Element Mesh Adaptation Strategy From Residual and Hierarchical Error Estimators in Eddy Current Problems

Dular, Patrick; Menach, Yvonnick Le; Tang, Zuqi; Creusé, Emmanuel; Piriou, F.

doi:10.1109/tmag.2014.2352553

Cited by 6 publications

(3 citation statements)

References 18 publications

(27 reference statements)

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“…Traditionally, it can be achieved by iteratively refining the mesh till the error introduced is minimized [22]. The refinement of the unstructured triangles can be done by employing edge bisection [23], point insertion, or by use of templates [24], [25]. These methods suffer from various problems like handling nonconformity, treatment of surrounding elements, generation of redundant elements, and over-refinement which leads to strict the Courant-Friedrichs-Lewy (CFL) condition in time-domain simulations [22].…”

Section: Accounting For Smart-mesh Strategymentioning

confidence: 99%

Smart-Mesh Strategy in DGTD Method for Partially Filled Cavity with Uncertain Interface Parameters

Li¹,

Hussain²,

Wang³

et al. 2020

RADIOENGINEERING

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To achieve high quality localization of nodes, a smart-mesh strategy is employed in the discontinuous Galerkin time-domain (DGTD) simulation. The strategy is able to adjust adaptively the nodes defined on the unstructured triangular element in real-time simulation, thus an arbitrary or uncertain shaped object can be modeled accurately. The benefits of smart-mesh strategy are demonstrated for a partially dielectric filled cavity with microscale random material height and uncertain rough interface. Numerical experiments show that the smart-mesh approach can capture fine structural information and achieve more effective positions to match variable shapes.

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Section: Accounting For Smart-mesh Strategymentioning

confidence: 99%

Smart-Mesh Strategy in DGTD Method for Partially Filled Cavity with Uncertain Interface Parameters

Li¹,

Hussain²,

Wang³

et al. 2020

RADIOENGINEERING

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“…Two error estimators have been presented for the MSFEM in the past, one based on hierarchical finite element spaces [5], based on the theory presented in [6] and [7], and one using flux equilibration [8], similar to this paper. However, both of them estimated only the error of the discrete MSFEM solution with respect to the continuous MSFEM solution.…”

Section: Introductionmentioning

confidence: 99%

An Equilibrated Error Estimator for the Multiscale Finite Element Method of a 2-D Eddy Current Problem

2021

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The multiscale finite element method is a valuable tool to solve the eddy current problem in laminated materials consisting of many iron sheets, which would be prohibitively expensive to resolve in a finite element mesh. It allows to use a coarse mesh which does not resolve each sheet and constructs the local fields using predefined micro-shape functions. This paper presents for the first time an a-posteriori error estimator for the multiscale finite element method which considers the error with respect to the exact solution. It is based on flux equilibration and a modification of the theorem of Prager and Synge and provides an upper bound for the error that does not include generic constants. Numerical examples show a good performance in both the linear and the nonlinear case.

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“…The others, based on a posteriori analysis, verify the quality of the obtained numerical solution. These a posteriori error estimators can be decomposed into three families: equilibrated error estimators (EEE) (Rikabi et al, 1988;Remacle et al, 1996;Marmin et al, 1998), hierarchical error estimators (HEE) (Dular, 2009;Dular et al, 2014) and residual error estimators (REE), (Beck et al, 2000;Nicaise and Creusé, 2003). With the EEE, it is possible to get a map of the local error directly linked to the exact solution (Tang et al, 2013b).…”

Section: Introductionmentioning

confidence: 99%

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

Tang

Menach

Creusé

et al. 2015

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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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Finite Element Mesh Adaptation Strategy From Residual and Hierarchical Error Estimators in Eddy Current Problems

Cited by 6 publications

References 18 publications

Smart-Mesh Strategy in DGTD Method for Partially Filled Cavity with Uncertain Interface Parameters

Smart-Mesh Strategy in DGTD Method for Partially Filled Cavity with Uncertain Interface Parameters

An Equilibrated Error Estimator for the Multiscale Finite Element Method of a 2-D Eddy Current Problem

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

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