Zuqi Tang

Residual-based a posteriori estimators for the A/phi magnetodynamic harmonic formulation of the Maxwell system

This paper is devoted to the derivation of an a posteriori residual-based error estimator for the A/phi magnetodynamic harmonic formulation of the Maxwell system. The weak continuous and discrete formulations are established, and the well-posedness of both of them is addressed. Some useful analytical tools are derived. Among them, an ad-hoc Helmholtz decomposition is proven, which allows to pertinently split the error. Consequently, an a posteriori error estimator is obtained, which is proven to be reliable and locally efficient. Finally, numerical tests confirm the theoretical results.

Residual and equilibrated error estimators for magnetostatic problems solved by finite element method

In finite element computations, the choice of the mesh is crucial to obtain accurate solutions. In order to evaluate the quality of the mesh, a posteriori error estimators can be used. In this paper, we develop residual-based error estimators for magnetostatic problems with both classical formulations in term of potentials used, as well as the equilibrated error estimator. We compare their behaviors on some numerical applications, to understand the interest of each of them in the remeshing process.

Energetic Galerkin Projection of Electromagnetic Fields Between Different Meshes

Mesh-to-mesh field transfer arises frequently in finite-element computations. Typical applications may concern remeshing, multigrid methods, domain decomposition, and multi-physics problems. For electromagnetic fields, one of the essential constraints in such transfers is to conserve energetic quantities such as magnetic energy and joule heating. Within the framework of Galerkin projection on overlapping domains, we introduce the definition of energetic norms for electromagnetic fields. The corresponding formulations we propose provide energy-conserving projection of electromagnetic fields between different meshes.

A posteriori error estimator for harmonic A‐φ formulation

Purpose – In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation.Design/methodology/approach – The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency).Findings – This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation.Originality/value – In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

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

A strategy of mesh adaptation in eddy current finite element modeling is developed from both residual and hierarchical error estimators. Wished distributions of element sizes of adapted meshes are determined from the element-wise local contributions to the estimators and define constraints for the mesh generator. Uniform distributions of the local error are searched.

Comparison of Residual and Hierarchical Finite Element Error Estimators in Eddy Current Problems

The finite element computation of eddy current problems introduces numerical error. This error can only be estimated. Among all error estimators (EEs) already developed, two estimators, called residual and hierarchical EEs, proven to be reliable and efficient, are theoretically and numerically compared. Both estimators show similar behaviors and locations of the error.

Residual-based a posteriori error estimation for stochastic magnetostatic problems

In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals.

Residual a Posteriori Estimator for Magnetoharmonic Potential Formulations With Global Quantities for the Source Terms

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/Ω harmonic formulations. The definitions of the estimators are given and some numerical examples are provided to show the behavior of the estimators.

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

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 ...