Fiche individuelle
Zuqi TANG | ||
Titre | MCF | |
Equipe | Outils et Méthodes Numériques | |
Adresse | Université de LILLE Avenue Paul langevin 59655 VILLENEUVE-D'ASCQ | |
Téléphone | +33 (0)3-622-68-230 | |
zuqi.tang@univ-lille.fr | ||
Site personnel | https://orcid.org/0000-0002-5402-5858 | |
Réseau scientifique | https://www.researchgate.net/profile/Zuqi_Tang | |
Observation / Thématique de recherche | Numerical analysis and scientific computing; AI and Deep learning technique; Darwin model; Computational electromagnetics | |
Publications |
ACLI Revue internationale avec comité de lecture |
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[1] Goal-oriented error estimation based on equilibrated flux and potential reconstruction for the approximation of elliptic and
parabolic problems Computers and Mathematics with Applications, 07/2023, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi |
We present a unified framework for goal-oriented estimates for elliptic and parabolic problems that combines the dual-weighted residual method with equilibrated flux and potential reconstruction. These frameworks allow to analyze simultaneously different approximation schemes for the space discretization of the primal and the dual problems such as conforming or nonconforming finite element methods, discontinuous Galerkin methods, or the finite volume method. Our main contribution is twofold: first in a unified framework we prove the splitting of the error into a fully computable estimator η and a remainder, second this remainder is estimated by the product of the fully computable energy-based error estimators of the primal and dual problems. Some illustrative numerical examples that validate our theoretical results are finally presented. |
[2] Optimal Sensor Placement via Parameterized Background Data Weak Method applied to Magnetostatic Problems including Anisotropy IEEE Transactions on Magnetics, Vol. 59, N°. 5, 05/2023, URL, Abstract ALAHYANE Mohamed, TANG Zuqi, BENABOU Abdelkader |
The need for electrical machines is growing in a wide range of applications nowadays, such as for energy production, automotive, marine, and medical equipment, etc. The reliability, efficiency, performance and operational safety are always critical issues, which implies that the monitoring and analysis during the operation of the equipment need to be strengthened. In general, more sensors can give higher accuracy of the estimated physical quantity, but bring a more expensive cost. To address this issue, an algorithm principally based on the parameterized background data-weak (PBDW) method is proposed and adopted in this work to optimize both the number and the location of sensors. Besides, to further investigate the performance of the proposed algorithm, a prototype concerning an anisotropic magnetostatic problem is studied as an example for the placement of magnetic sensors. The numerical experiments shows that the proposed method can achieve very satisfactory results in different aspects. |
[3] Electromagnetic Modeling of PCB Based on Darwin's Model Combined With Degenerated Prism Whitney Elements IEEE Transactions on Power Electronics, Vol. 38, N°. 1, pages. 678-691, 01/2023, URL, Abstract TAHA Houssein, HENNERON Thomas, TANG Zuqi, LE MENACH Yvonnick, PACE Loris, DUCREUX Jean-Pierre |
Due to the advancement in the development of semiconductors used in the power converters, the printed circuit boards (PCBs) require an in-depth study of their electromagnetic behavior. To characterize the behavior of the PCBs, the Darwin model is employed, which can take into account all the coupled effects, namely resistive, inductive, and capacitive effects, at the intermediate frequencies. Nevertheless, the study of particular structures having a geometric dimension smaller than the others can create meshing difficulties. The modeling of thin structures by the finite element method requires the optimization of the mesh. To circumvent this issue, the shell elements for both node and edge elements are applied in this work. Finally, to validate the proposed approaches, two PCBs with different geometries are studied in both time and frequency domains, where the measurements for a single PCB are provided to compare with the numerical results. |
[4] Investigation of the correlation between NDT signatures of low carbon content martensitic steels and their tensile properties Journal of Magnetism and Magnetic Materials (JMMM), Vol. 563, pages. 169995, 12/2022, URL, Abstract DHERBÉCOURT Marwane, MESSAL Oualid, TANG Zuqi, BENABOU Abdelkader, LAZZARI Olivier |
Nondestructive testing (NDT) of industrial steel products is commonly used to detect defects such as cracks using among other methods, electromagnetic techniques. When properly calibrated, these NDT can be adapted to evaluate the mechanical properties of steels. It is especially of prime importance when rigorous quality control must be achieved for high performance steels. In this context, the proposed article deals with the investigation of the Magnetic Barkhausen Noise (MBN) to characterize the tensile properties of high mechanical performance martensitic steels. |
[5] Further investigation of convolutional neural networks applied in computational electromagnetism under physics-informed consideration IET Electric Power Applications, Vol. 16, N°. 6, pages. 653-674, 04/2022, URL, Abstract GONG Ruohan, TANG Zuqi |
Convolutional neural networks (CNN) have shown great potentials and have been proven to be an effective tool for some image-based deep learning tasks in the field of computational electromagnetism (CEM). In this work, an energy-based physics-informed neural network (EPINN) is proposed for low-frequency electromagnetic computation. Two different physics-informed loss functions are designed. To help the network focus on the region of interest instead of computing the whole domain on average, the magnetic energy norm error loss function is proposed. Besides, the methodology of energy minimization is integrated into the CNN by introducing the magnetic energy error loss function. It is observed that the introduction of the physics-informed loss functions improved the accuracy of the network with the same architecture and database. Meanwhile, these changes also cause the network to be more sensitive to some hyperparameters and makes the training process oscillate or even diverge. To address this issue, the sensitivity of the network hyperparameters for both physics-informed loss functions are further investigated. Numerical experiments demonstrate that the proposed approaches have good accuracy and efficiency with fine-tuned hyperparameters. Furthermore, the post-test illustrates that the EPINN has excellent interpolation performance and can obtain good extrapolation results under certain restrictions. |
[6] Improvement of CNN based Anisotropic Magnetostatic Field Computation via Adaptive Data Subset Selection IEEE Transactions on Magnetics, 03/2022, Abstract GONG Ruohan, TANG Zuqi |
A numerical issue arises when we extend the convolutional neural network (CNN) U-net to the anisotropic magnetostatic field computation. The output magnetic field has a significant gradient with respect to the input geometry parameter, which introduces inevitable errors in the training process to degrade the performance of deep learning (DL). To address this issue, the subset selection approach is utilized to divide the whole database into serval subsets, where the samples are assigned according to the gradient between the input and output. Then these subsets with different sample densities are combined into a global one. Taking the uniform dataset with the same sample size as a comparison, the influence of subset selection on DL is investigated by comparing the performance of CNN on different datasets. Numerical experiments illustrate that the adaptive subset selection can be employed to improve the accuracy and efficiency of the CNN network. |
[7] Stabilized Gauged Formulation of Darwin Model for FEM Computation of Industrial Applications IEEE Transactions on Magnetics, Vol. 58, N°. 9, 03/2022, URL, Abstract TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, DUCREUX Jean-Pierre, SALOMEZ Florentin |
The Darwin model, which simultaneously incorporates resistive, capacitive, and inductive effects but neglects the radiation one, has recently attracted more and more attention in the research area. For our industrial application needs, the finite-element (FE) system to solve derived from the Darwin model generally has a large size, which is beyond the capabilities of the direct solvers due to the memory limitation. In this work, a specially designed formulation amenable to an iterative solver is proposed for industrial applications. Moreover, a detailed comparison of different cases is carried out on two different examples. |
[8] Numerical Simulation-Based Investigation of the Limits of Different Quasistatic Models Applied Sciences, Vol. 11, N°. 23, pages. 11218, 11/2021, URL, Abstract TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, SALOMEZ Florentin, DUCREUX Jean-Pierre |
The modeling of the capacitive phenomena, including the inductive effects becomes critical, especially in the case of a power converter with high switching frequencies, supplying an electrical device. At a low frequency, the electro-quasistatic (EQS) model is widely used to study the coupled resistive-capacitive effects, while the magneto-quasistatic (MQS) model is used to describe the coupled resistive-inductive effects. When the frequency increases, the Darwin model is preferred, which is able to capture the coupled resistive-capacitive-inductive effects by neglecting the radiation effects. In this work, we are interested in specifying the limits of these models, by investigating the influence of the frequency on the electromagnetic field distributions and the impedance of electromagnetic devices. Two different examples are carried out. For the first one, to validate the Darwin model, the measurement results are provided for comparison with the simulation results, which shows a good agreement. For the second one, the simulation results from three different models are compared, for both the local field distributions and the global impedances. It is shown that the EQS model can be used as an indicator to know at which frequency the Darwin model should be applied. |
[9] Fast Time-domain Solution of Dynamic Electromagnetic Problems based on Sinc Interpolation IEEE Transactions on Magnetics, Vol. 57, N°. 6, 06/2021, URL, Abstract GUO Ze, WANG Shuhong, TANG Zuqi, REN Zhuoxiang |
In time domain electromagnetic field problems that have a fast time response with sharp field change or need a long time transient process to get the steady-state solution, a large number of time step iterations are required using the classical time-stepping method. A reduced model based on Sinc interpolation is proposed in this work. The accuracy of the proposed method does not depend on the traditional time-domain discretization step but only the number of sampling points. Two numerical examples, namely an electro-quasistatic problem and a field-circuit coupled problem, are considered to illustrate the accuracy and performance of the proposed method. It is shown that only a few pre-computed samplings are sufficient to obtain a good performance in comparing with the traditional time-stepping method. |
[10] Training Sample Selection Strategy applied to CNN in Magneto-Thermal coupled Analysis IEEE Transactions on Magnetics, Vol. 57, N°. 6, 06/2021, URL, Abstract GONG Ruohan, TANG Zuqi |
Deep learning (DL) has attracted more and more attention in computational electromagnetism. Particularly, the Convolutional Neural Network (CNN) is one of the most popular learning models in DL due to its excellent capacity for feature extraction and convergence. The efficiency of CNN mainly depends on how many training samples are needed to effectively converge the network. The sample preparation process often involves a lot of numerical computations, which can be very expensive and time-consuming. In this paper, based on the traditional DL network training procedure, two different approaches, namely adding smart training samples and reference samples, are proposed to help the DL network converge. The smart sample selection is based on a greedy algorithm, which can be applied for both training and reference samples. The influences of these two approaches on the CNN training process are investigated by an example of the coupled magneto-thermal computation applied to a transformer. Numerical results show that the two proposed approaches can significantly help the network to converge and improve the efficiency of the DL model. |
[11] Guaranteed Quantity of Interest Error Estimate Based on Equilibrated Flux Reconstruction IEEE Transactions on Magnetics, Vol. 57, N°. 6, pages. 7402104, 06/2021, URL, Abstract TANG Zuqi, LOU Suyang, BENABOU Abdelkader, CREUSE Emmanuel, NICAISE Serge, KORECKI Julien, MIPO Jean-Claude |
The quality of a local physical quantity obtained by the numerical method such as the finite element method (FEM) attracts more and more attention in computational electromagnetism. Inspired by the idea of goal-oriented error estimate given for the Laplace problem, this work is devoted to a guaranteed a posteriori error estimate adapted for the quantity of interest (QOI) linked to magnetostatic problems, in particular, to the value of the magnetic flux density. The development is principally based on an equilibrated flux construction, which ensures fully computable estimators without any unknown constant. The main steps of the mathematical development are given in detail with the physical interpretation. An academic example using an analytical solution is considered to illustrate the performance of the approach, and a discussion about different aspects related to the practical point of view is proposed. |
[12] Investigation of Convolutional Neural Network U-net under Small Datasets in Transformer Magneto-Thermal Coupled Analysis The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 39, N°. 4, pages. 959-970, 08/2020, URL, Abstract GONG Ruohan, TANG Zuqi |
This paper aims to investigate the approach combine the deep learning (DL) and finite element method for the magneto-thermal coupled problem. |
[13] Structure-Preserved Reduced Order Modeling for Frequency Domain Solution of the Darwin Model with a Gauged Potential Formulation IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 1-4, 01/2020, URL, Abstract YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang |
In this work, the proper orthogonal decomposition (POD) is applied for parametric analysis in the gauged potential formulation of the Darwin model considering both capacitive and inductive effects. Due to the large contrast in material parameters, the resulted system matrix is ill-conditioned. Also, the condition number of the corresponding snapshot complex matrix is very huge. To improve the stability of the POD method, a structured-preserving strategy is considered and implemented for different unknown potentials, namely the magnetic vector potential A, the electric scalar potential φ, and the Lagrange multiplier p. Besides, a greedy algorithm is proposed to select the snapshots adaptively. Two numerical examples, including a parallel plate capacitor and a modified RLC device structure, are provided to illustrate the capability of proposed POD in model order reduction in frequency domain solvers. |
[14] Residual Type a posteriori Error Estimates for 3-D Low Frequency Stable Maxwell Formulations in Both Frequency and Time Domains IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 1-4, 01/2020, URL, Abstract TANG Zuqi, ZHAO Yanpu |
In this paper, residual type a posteriori error estimates developed in our previous work for magnetostatic and eddy current problems are extended to low-frequency (LF) Maxwell problems using A/φ formulation, where both inductive and capacitive effects can be handled simultaneously. Classical low order finite element basis (LOFEB), as well as high order finite element basis (HOFEB) of edge and nodal type are adopted in numerical examples to evaluate the performance of the proposed estimators. |
[15] Proper Generalized Decomposition for Edge Elements in Magnetostatics with Adaptive Stopping Criterion IEEE Transactions on Magnetics, Vol. 56, N°. 1, pages. 1-4, 01/2020, URL, Abstract YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang |
The proper generalized decomposition (PGD) is ana priorimodel order reduction (MOR) method based on a variable-separatedexpression of the problem. Two iterative loops are needed in the PGD algorithm, namely the outer loop for enriching the reductionmodes progressively, and the inner loop for solving each mode by fixed point iterations. Setting the stopping criterion of these twoloops blindly can cause either the inaccuracy of the PGD or a waste of iterations. In this work, a special variable-separated PGDwith edge elements is proposed and implemented on a hexahedral mesh in magnetostatics. Also, an adaptive stopping criterion basedon dual formulations is applied to balance different error components, namely the discretization error, error for outer and innerloops of PGD. A numerical example is given to illustrate the proposed approach |
[16] An Improved Newton Method Based on Choosing Initial Guess Applied to Scalar Formulation in Nonlinear Magnetostatics IEEE Transactions on Magnetics, Vol. 55, N°. 6, pages. 1-4, 06/2019, URL, Abstract CHERIF Riheb, TANG Zuqi, GUYOMARCH Frédéric, CHEVALLIER Loïc, LE MENACH Yvonnick |
An improved starting point Newton method applied to 3-D scalar formulation in magnetostatics is proposed in this paper. Compared with the classical Newton method, the inexact-Newton and quasi-Newton methods are reported by testing on a benchmark problem as well as an industrial example. Remarkable convergence acceleration using the proposed strategy is observed, and thus, it significantly
reduces the computational time. |
[17] A Symmetric Field-circuit Coupled Formulation for 3-D Transient Full-wave Maxwell Problems IEEE Transactions on Magnetics, Vol. 55, N°. 6, pages. 1-4, 06/2019, URL, Abstract ZHAO Yanpu, TANG Zuqi |
In this paper, a symmetric field-circuit coupled finite element method (FEM) for low-frequency (LF) full-wave Maxwell problems using a magnetic vector potential (MVP) formulation is proposed. The resultant fully-discrete coefficient matrix is made symmetric for the first time by introducing the so-called source electric scalar potential (ESP) for solid conductors, where the terminal currents are converted from surface integrations of the current density vectors to volumetric integrations. Numerical examples, including a benchmark capacitor charging problem with external circuit connections, are solved and the numerical results match well with reference solutions. The proposed formulation is useful when analyzing electromagnetic fields with coupled inductive-capacitive effects and external circuit connections. |
[18] A Novel Gauged Potential Formulation for 3-D Electromagnetic Field Analysis Including Both Inductive and Capacitive Effects IEEE Transactions on Magnetics, Vol. 55, N°. 6, 06/2019, URL, Abstract ZHAO Yanpu, TANG Zuqi |
In this paper, a novel potential formulation for low-frequency (LF) applications taking into account both inductive and capacitive effects but without considering wave propagation is proposed. Both time-domain and frequency-domain formulations are presented.
The resultant fully discrete finite-element matrix is made symmetric by incorporating a gauge condition and also rewriting the current continuity equation. To improve numerical accuracy and computational efficiency, high-order mixed-edge elements and nodal elements are adopted to approximate the vector and scalar unknown variables together with high-order time-stepping schemes. Several numerical examples are solved to validate and showcase the accuracy of the proposed methods. The proposed formulations are stable in use for LF electromagnetic field computations by considering inductive and capacitive effects simultaneously, such as finding the resonant frequencies of wireless power transfer devices. |
[19] Accurate Extraction of Winding Inductances using Dual Formulations without Source Field Computation IEEE Transactions on Magnetics, Vol. 55, N°. 6, pages. 1-4, 06/2019, URL, Abstract ZHAO Yanpu, TANG Zuqi |
Dual formulations are accurate in use for computing energy-related global quantities such as inductance and providing upper and lower bounds of the unknown true values of these global parameters, which is not possible if using a single formulation. Since traditional dual formulations result in totally different algebraic matrix equations, people have to develop two different finite element programs and solve the resultant two algebraic equation systems respectively. In this work two practical dual formulations
for open region magnetostatic problems, where the global finite element matrices are exactly the same, are adopted for extracting the winding inductances. Finite element formulation and implementation details are presented. Practical examples having complex windings are solved using the proposed methods to showcase the effectiveness and accuracy. High order FE basis functions are also used to enhance the solution accuracy. The proposed method is highly useful for medium-sized industrial applications by providing guaranteed inductance parameters. |
[20] Improved Equilibrated Error Estimates for Open Boundary Magnetostatic Problems Based on Dual A and H Formulations IEEE Transactions on Magnetics, Vol. 55, N°. 6, pages. 1-5, 06/2019, URL, Abstract ZHAO Yanpu, TANG Zuqi |
Calculating the bounds of global energy is an important issue in computational electromagnetism, which can provide guaranteed results when extracting inductance parameters. In this paper, an improved equilibrated type a posteriori error estimate for open boundary magnetostatic problems is proposed. We derive our error estimator based on vector dual formulations, which can be efficiently solved using parallel sparse direct solvers. The new estimator can provide a sharp and guaranteed estimate of the finite-element spatial discretization error. Moreover, the computational cost is cheaper than using existing equilibrated error estimators. Numerical experiments are carried out to showcase the performance of our error estimator, including the modified TEAM workshop problem 13 and the benchmark IEEJ problem. |
[21] Auto-Gauging of Vector Potential by Parallel Sparse Direct Solvers–Numerical Observations IEEE Transactions on Magnetics, Vol. 55, N°. 6, pages. 1-4, 06/2019, URL, Abstract TANG Zuqi, ZHAO Yanpu, REN Zhuoxiang |
When using magnetic vector potential (MVP)-based formulations for magnetostatic or eddy-current problems, either gauge conditions specifying the divergence of the MVP or tree gauging by eliminating redundant degrees of freedom of the MVP is usually imposed to ensure uniqueness of solutions. Explicit gauging of the MVP is not always necessary since classical iterative solvers can automatically and implicitly fix the gauge as long as the right-hand side vectors are consistent. Besides iterative solvers, implicit gauging is also observed when using state-of-the-art parallel sparse direct solvers (PSDSs), thanks to the built-in functions of handling null-spaces of either real symmetric positive semi-definite matrix systems or those complex symmetric systems from eddy-current problems. Both static and eddy-current examples are solved by PSDS to demonstrate results of local physical quantities or global quantities such as magnetic energy or joule losses. High-order edge/nodal elements are also considered in our numerical examples and it is observed that PSDS can also easily and correctly handle the delicate discrete null spaces. |
[22] Multiscale modeling of magnetic distribution of ribbon magnetic cores CES Transactions on Electrical Machines and Systems, Vol. 2, N°. 4, pages. 425 - 429, 12/2018, URL LI Hailin, TANG Zuqi, WANG Shuhong, ZHU Jianguo |
[23] Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem Numerische Mathematik, Vol. 138, N°. 4, pages. 1027–1065, 04/2018, URL, Abstract ČERMÁK Martin, HECHT Frédéric, TANG Zuqi, VOHRALÍK Martin |
In this paper, we develop adaptive inexact versions of iterative algorithms applied to finite element discretizations of the linear Stokes problem. We base our developments on an equilibrated stress a posteriori error estimate distinguishing the different error components, namely the discretization error component, the (inner) algebraic solver error component, and possibly the outer algebraic solver error component for algorithms of the Uzawa type. We prove that our estimate gives a guaranteed upper bound on the total error, as well as a polynomial-degree-robust local efficiency, and this on each step of the employed iterative algorithm. Our adaptive algorithms stop the iterations when the corresponding error components do not have a significant influence on the total error. The developed framework covers all standard conforming and conforming stabilized finite element methods on simplicial and rectangular parallelepipeds meshes in two or three space dimensions and an arbitrary algebraic solver. Implementation into the FreeFem++ programming language is invoked and numerical examples showcase the performance of our a posteriori estimates and of the proposed adaptive strategies. As example, we choose here the unpreconditioned and preconditioned Uzawa algorithm and the preconditioned minimum residual algorithm, in combination with the Taylor–Hood discretization. |
[24] Modeling of Magnetic-Induced Deformation Using Computer Code Chaining and Source-Tensor Projection IEEE Transactions on Magnetics, Vol. 53, N°. 6, pages. 1–4, 06/2017, URL, Abstract LIU Mingyong, TANG Zuqi, MININGER Xavier, BOUILLAULT Frédéric, HUBERT Olivier, BERNARD Laurent |
Source tensor projections are developed for the magneto-elastic coupled problems when magnetostriction-induced force and magnetic force are considered. Comparisons with classical force density projection are first performed on a simple example. Then, it is investigated on an application of a multilayer transformer core with the consideration of material anisotropy and multilayer inhomogeneity. |
[25] Residual-based a posteriori estimators for the potential formulations of electrostatic and time-harmonic eddy current problems with voltage or current excitation International Journal for Numerical Methods in Engineering, Vol. 107, N°. 5, pages. 377--394, 08/2016, URL, Abstract CHEN Chao, CREUSE Emmanuel, NICAISE Serge, TANG Zuqi |
In this paper, we consider some potential formulations of electrostatic as well as time-harmonic eddy current problems with voltage or current excitation sources. The well-posedness of each formulation is first established. Then, the reliability of the corresponding residual-based a posteriori estimators is derived in the context of the finite element method approximation. Finally, the implementation in an industrial code is performed, and the obtained theoretical results are illustrated on an academic and on an industrial benchmark. |
[26] Residual a posteriori error estimation for a stochastic magnetostatic problem Journal of Computational and Applied Mathematics, Vol. 289, pages. 51--67, 12/2015, URL, Abstract MAC Duy Hung, TANG Zuqi, CLENET Stéphane, CREUSE Emmanuel |
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. |
[27] A posteriori residual error estimators with mixed boundary conditions for quasi-static electromagnetic problem The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 34, N°. 3, pages. 724-739, 07/2015, URL TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis, NEMITZ Nicolas |
[28] Residual a posteriori estimator for magnetoharmonic potential formulations with global quantities for the source terms IEEE Transactions on Magnetics, Vol. 51, N°. 3, 06/2015, URL, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
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. |
[29] Finite element mesh adaptation strategies from residual and hierarchical error estimators in eddy current problems IEEE Transactions on Magnetics, Vol. 51, N°. 3, 04/2015, URL, Abstract DULAR Patrick, LE MENACH Yvonnick, TANG Zuqi, CREUSE Emmanuel, PIRIOU Francis |
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. |
[30] Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system Mathematical Methods in the Applied Sciences, Vol. 38, N°. 4, pages. 738--750, 02/2014, URL, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi |
This paper is devoted to the derivation of a Helmholtz decomposition of vector fields in the case ofmixed boundary conditions imposed on the boundary of the domain. This particular decomposition allows to obtain a residual a posteriori error estimator for the approximation ofmagnetostatic problems given in the so-called A-formulation, for which the reliability can be established. Numerical tests confirm the obtained theoretical predictions. |
[31] Comparison of Residual and Hierarchical Finite Element Error Estimators in Eddy Current Problems IEEE Transactions on Magnetics, Vol. 50, N°. 2, pages. 501-504, 02/2014, URL, Abstract DULAR Patrick, TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, PIRIOU Francis |
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. |
[32] Energetic Galerkin Projection of Electromagnetic Fields Between Different Meshes IEEE Transactions on Magnetics, Vol. 50, N°. 2, pages. 613-616, 02/2014, URL, Abstract WANG Zifu, TANG Zuqi, HENNERON Thomas, PIRIOU Francis, MIPO Jean-Claude |
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 the magnetic energy and the 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. |
[33] Residual and equilibrated error estimators for magnetostatic problems solved by finite element method IEEE Transactions on Magnetics, Vol. 49, N°. 12, pages. 5715 - 5723, 12/2013, URL, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
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. |
[34] A posteriori error estimator for harmonic A-Phi formulation The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32, N°. 4, pages. 1219 - 1229, 07/2013, URL, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
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. |
[35] Residual based a posteriori error estimators for harmonic A/Phi and T/Omega formulations in eddy current problems IEEE Transactions on Magnetics, Vol. 49, N°. 5, pages. 1721 - 1724, 05/2013, URL, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
For eddy current problems, potential formulations are widely used nowadays. In this paper, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A /φ and T /Ω harmonic formulations. A device with eddy currents is studied in order to show the efficiency of the proposed estimators. |
[36] Residual-based a posteriori estimators for the T/Omega magnetodynamic harmonic formulation of the Maxwell system International Journal of Numerical Analysis and Modeling, Vol. 10, N°. 2, pages. 411-429, 02/2013, URL, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi, LE MENACH Yvonnick, NEMITZ Nicolas, PIRIOU Francis |
In this paper, we focus on an a posteriori residual-based error estimator for the T/Omega
magnetodynamic harmonic formulation of the Maxwell system. Similarly to the A/Phi formulation, 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 for the T/Omega
case is derived, 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. |
[37] Residual-based a posteriori estimators for the A/Phi magnetodynamic harmonic formulation of the Maxwell system Mathematical Models and Methods in Applied Sciences, Vol. 22, N°. 5, pages. 30, 05/2012, URL, Abstract CREUSE Emmanuel, NICAISE Serge, TANG Zuqi, LE MENACH Yvonnick, NEMITZ Nicolas, PIRIOU Francis |
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. |
ACT Conférence internationale avec acte |
[1] Improved ODF approach to model magnetic properties of Grain Oriented Electrical Steels taking into account mechanical stress 26th Soft Magnetic Materials Conference, Prague, Czech Republic, 09/2023, 09/2023 LI Zhenxin, TANG Zuqi, MESSAL Oualid, BENABOU Abdelkader, WANG Shuhong |
[2] Comparison of PBDW and Maxvol algorithms for the optimal sensor placement COMPUMAG2023, Kyoto, Japon, 05/2023, 05/2023 ALAHYANE Mohamed, TANG Zuqi, BENABOU Abdelkader |
[3] MOR or DL, a comparison from the aspect of the surrogate model constructions 11th International Conference on Computation in Electromagnetics, CEM2023, 11-14 April, Cannes, France, 12/2022, Abstract GONG Ruohan, TANG Zuqi, HENNERON Thomas |
In this paper, a comparison between the model order reduction technique and deep learning technique is proposed, from the aspect of the surrogate model construction in computational electromagnetism. The merit and demerit of both approaches are discussed and compared via an academic application of magneto-thermal coupled analysis. |
[4] Hot Spot Driven Physics-informed Neural Network via Special Designed Quantity of Interest applied to Magneto-thermal Analysis CEFC 2022, October 9 - 12, 2022 - Denver, Colorado, 10/2022 GONG Ruohan, TANG Zuqi |
[5] Optimal Sensor Placement via Parameterized Background Data-Weak Method applied to Magnetostatic Problems including Anisotropy CEFC 2022, October 9 - 12, 2022 - Denver, Colorado, 10/2022, 10/2022 ALAHYANE Mohamed, TANG Zuqi, BENABOU Abdelkader |
[6] Effet de la préparation de surface sur les réponses CND électromagnétiques d'aciers martensitiques Conférence Matériaux 2022, 10/2022 DHERBÉCOURT Marwane, MESSAL Oualid, TANG Zuqi, BENABOU Abdelkader |
[7] Determination of the Limits of Different Quasistatic Models Based on Multi-Domains Application EPNC 2022, Hamburg, Allemagne, 07/2022 TAHA Houssein, LE MENACH Yvonnick, HENNERON Thomas, TANG Zuqi, DUCREUX Jean-Pierre |
[8] Correlation between NDT signatures of steels and their tensile properties 25th Soft Magnetic Materials Conference, Grenoble, France, 05/2022, Abstract DHERBÉCOURT Marwane, MESSAL Oualid, TANG Zuqi, BENABOU Abdelkader, LAZZARI Olivier |
Electromagnetic non-destructive testing (NDT) of industrial steels is mostly employed to detect defects such as cracks or mechanical properties inhomogeneities. However, NDT can also be employed, when properly calibrated, to evaluate quantitatively these mechanical properties. It is especially of interest when rigorous quality testing must be achieved on finished steel-based products of which mechanical characteristics must be guaranteed. In that context, the proposed work deals with the evaluation of electromagnetic NDT to characterize the tensile properties of high mechanical performance steels. |
[9] Deep learning Using Domain Decomposition Method Applied to Anisotropy Magnetostatics problem COMPUMAG 2021,Cancun, Mexico, 16th-20th January 2022, 01/2022 GONG Ruohan, TANG Zuqi |
[10] Improved Sinc Method Based on POD Technique for Time Domain Electromagnetic Field Problems COMPUMAG 2021, Cancun, Mexico, 16th-20th January 2022, 01/2022 GUO Ze, TANG Zuqi, YAN Shuai, REN Zhuoxiang |
[11] Comparison of iterative and direct solvers in the solving of different considerations of Darwin formulations COMPUMAG 2021, Cancun, Mexico, 16th-20th January 2022, 01/2022, Abstract TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, DUCREUX Jean-Pierre |
The modeling of the capacitive phenomena including the inductive effects becomes critical, especially in the case of a power converter with high switching frequencies supplying an electrical device. To capture the coupled capacitive-inductive effects, the Darwin model is invoked in the frequency domain, which only neglects the radiation effects of the full Maxwell system. In this work, we are interested in the comparison of the different solvers, both iterative and direct, for ungauged and gauged finite-element (FE) systems for Darwin model. In addition, to handle the huge FE resulting matrix due to the industrial application, a novel formulation is proposed. |
[12] Application of degenerated prism Whitney elements in the modeling of PCB using Darwin model EMF 2021, Marseille, France, 6-8 July 2021, 06/2021 TAHA Houssein, HENNERON Thomas, TANG Zuqi, LE MENACH Yvonnick, DUCREUX Jean-Pierre |
[13] Small Data Sets Deep Learning based on DCGAN for Magnetic Field CEFC 2020, Nov 16-18, 2020 – Pisa, Italy, 11/2020 GONG Ruohan, ZHOU Xiangchun, LI Yue, CUI Tao, TANG Zuqi |
[14] Training Sample Selection Strategy Applied To Convolutional Neural Network In Magneto-Thermal Coupled Analysis CEFC 2020, Nov 16-18, 2020 – Pisa, Italy, 11/2020 GONG Ruohan, TANG Zuqi |
[15] Guaranteed Quantity Of Interest Error Estimate Based On Equilibrated Flux Reconstruction CEFC 2020, Piza, Italy, 11/2020, 11/2020 TANG Zuqi, LOU Suyang, BENABOU Abdelkader, CREUSE Emmanuel, NICAISE Serge, KORECKI Julien, MIPO Jean-Claude |
[16] Numerical Simulation In Voltage Withstand Using Quasistatic and Darwin Models CEFC 2020, Pisa, Italy, 16-18 November, 2020, 11/2020 TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, DUCREUX Jean-Pierre |
[17] Numerical Simulation of Surge Arrester using Nonlinear Electro-Quasistatic Formulation EPNC 2020, Torino, Italy, 30 June - 3 July 2020,, 06/2020 TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, DUCREUX Jean-Pierre |
[18] Adaptive Stopping Criterion of PGD for Edge Elements based on Equilibrated Error Estimates in Magnetostatic Problems COMPUMAG 2019, Paris, France, 07/2019 YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang |
[19] Structure-Preserved POD for Parametric Low Frequency Fullwave Problems with Gauged Potential Formulations COMPUMAG 2019, Paris, France, 07/2019 YAN Shuai, TANG Zuqi, HENNERON Thomas, REN Zhuoxiang |
[20] Convolutional Neural Network U-net applied in Transformer Multi-physics Analysis COMPUMAG 2019, Paris, France, 07/2019 GONG Ruohan, TANG Zuqi |
[21] Residual Type a posteriori Error Estimates for 3-D Low Frequency Stable Maxwell Formulations in Both Frequency and Time Domains COMPUMAG 2019, Paris, France, 07/2019 TANG Zuqi, ZHAO Yanpu |
[22] 3D coupled electromagnetic-fluid-thermal analysis and experiment of 10kV oil-immersed triangular wound core transformer 2019 Joint MMM-Intermag, January 14-18, 2019 Washington, DC, 01/2019 GONG Ruohan, TANG Zuqi, WANG Shuhong, HENNERON Thomas, RUAN Jiangjun |
[23] An Improved Newton Method Based on choosing Initial Guess Applied to Scalar Potential Formulation in Nonlinear Magnetostatics CEFC 2018, Hangzhou, China, 10/2018 CHERIF Riheb, TANG Zuqi, GUYOMARCH Frédéric, CHEVALLIER Loïc, LE MENACH Yvonnick |
[24] Application of U-Net Network and Training Strategy to Optimal Mesh Refinement in Computational Electromagnetism CEFC 2018, Hangzhou, China, 10/2018 TANG Zuqi, SHEN Xi, HENNERON Thomas |
[25] Calibration of a Miniature Single Sheet Tester with Guaranteed FE-simulation CEFC 2018, Hangzhou, China, 10/2018 TANG Zuqi, BENABOU Abdelkader, ZHAO Yanpu |
[26] Application of FreeFem++ Programming Language for 3D Electromagnetic Field Simulations CEFC 2018, Hangzhou, China, 10/2018 TANG Zuqi, ZHAO Yanpu, HECHT Frédéric |
[27] An improved starting point for Newton’s method solving 3D nonlinear magnetostatic problems EPNC 2018, Arras, France, 06/2018 CHERIF Riheb, TANG Zuqi, GUYOMARCH Frédéric, CHEVALLIER Loïc, LE MENACH Yvonnick |
[28] Gauged Dual Formlations for Fast and Accurate Computation of Inductance Parameters of Magnetostatics Problems EMF 2018, Darmstadt, Germany, 04/2018 ZHAO Yanpu, TANG Zuqi |
[29] Dual Regularized Formulations for Open Boundary Magnetostatic Problems EMF 2018, Darmstadt, Germany, 04/2018 ZHAO Yanpu, TANG Zuqi |
[30] 3D modeling of magneto-elastic behavior using simplified multi-scale model: Application on power transformer core COMPUMAG 2017, Daejeon, Korea, 06/2017 TANG Zuqi, LIU Mingyong, BOUILLAULT Frédéric, MININGER Xavier, HUBERT Olivier |
[31] Vibration Prediction of Non-Oriented Silicon Iron Power Transformer Core under DC Bias COMPUMAG 2017, Daejeon, Korea, 06/2017 LIU Mingyong, HUBERT Olivier, TANG Zuqi, BOUILLAULT Frédéric, MININGER Xavier, BERNARD Laurent |
[32] Adaptive Stopping Criteria for Iterative Solver Applied to Potential Formulations in Magnetostatic Problems COMPUMAG 2017, Daejeon, Korea, 06/2017 TANG Zuqi |
[33] A posteriori error estimators for A and Ω magnetostatic formulations based on equilibrated fluxes reconstructions COMPUMAG 2017, Daejeon, Korea, 06/2017 TANG Zuqi |
[34] Error estimation in the computation of induced currents of human body 2013 CIGRE SC-C3 & EMF-ELF Colloquium, Japan, 10/2013 LELONG Thomas, TANG Zuqi, SCORRETTI Riccardo, THOMAS Pierre, LE MENACH Yvonnick, CREUSE Emmanuel |
[35] Energetic Galerkin projection of electromagnetic fields between different meshes
COMPUMAG 2013 Budapest, Hungary, 07/2013, Abstract WANG Zifu, TANG Zuqi |
The Galerkin projection provides an useful tool to transfer electromagnetic fields between different meshes.
Given an electromagnetic field calculated on the source mesh, the transfer to a different mesh can be employed for model-coupling, domain decomposition, remeshing, visualization and similar proposes.
The Galerkin projection consists of calculating a target field which minimizes the interpolation error between two discretized fields.
However, the $L^2$ Galerkin projection suffers from non-conservation of the electromagnetic energy.
In this paper, we present an energetic approach for Galerkin projections. |
[36] Error estimation in the Computation of Induced Current of Human Body in the Case of Low frequency Magnetic Field Excitation COMPUMAG 2013 Budapest, Hungary, 07/2013 LELONG Thomas, TANG Zuqi, SCORRETTI Riccardo, THOMAS Pierre, LE MENACH Yvonnick |
[37] Energetic Galerkin projection of electromagnetic fields between different meshes
COMPUMAG 2013 Budapest, Hungary, 07/2013, Abstract HENNERON Thomas, PIRIOU Francis, MIPO Jean-Claude |
The Galerkin projection provides an useful tool to transfer electromagnetic fields between different meshes.
Given an electromagnetic field calculated on the source mesh, the transfer to a different mesh can be employed for model-coupling, domain decomposition, remeshing, visualization and similar proposes.
The Galerkin projection consists of calculating a target field which minimizes the interpolation error between two discretized fields.
However, the $L^2$ Galerkin projection suffers from non-conservation of the electromagnetic energy.
In this paper, we present an energetic approach for Galerkin projections. |
[38] Error estimation in the Computation of Induced Current of Human Body in the Case of Low frequency Magnetic Field Excitation COMPUMAG 2013 Budapest, Hungary, 07/2013 CREUSE Emmanuel |
[39] Comparison of Residual and Hierarchical Finite Element Error
Estimators in Eddy Current Problems COMPUMAG 2013 Budapest, Hungary, 07/2013, URL, Abstract TANG Zuqi, DULAR Patrick, LE MENACH Yvonnick, CREUSE Emmanuel, PIRIOU Francis |
The finite element computation of eddy current
problems gives numerical error. This error cannot be calculated,
but can only be estimated. Among all error estimators already
developed, it is proposed to compare two proven estimators
called residual and hierarchical error estimators. |
[40] Residual based a posteriori error estimator for harmonic A-Phi and T-Omega formulation in eddy current problems CEFC 2012 Oita, Japan, 11/2012, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
For the eddy current problem, the potential formulations are widely used today. In this communication, residual based a posteriori error estimators are introduced to evaluate the discretization error in the finite element calculation in both case of A-Phi and T-Omega harmonic formulations. An example is carried out to show the behavior of our estimators. |
[41] A posteriori error estimator for harmonic A-Phi formulation EPNC 2012 Pula, Croatia, 06/2012, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
In this paper a residual-based error estimator is proposed 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-Phi formulation. This estimator is based on the evaluation of quantities weakly verified by the formulation. Furthermore as this estimator verifies the notions of reliability and efficiency it allows to estimate the qualities of local and global solutions. Two examples of electromagnetic systems with current density induced are used to show the efficiency of the proposed estimator. |
[42] A time-domain implicit-schema direct solver: application to finite integration solution ISEF 2011, 09/2011, Abstract WANG Zifu, LE MENACH Yvonnick, TANG Zuqi, KORECKI Julien, HENNERON Thomas |
In time-domain electromagnetic fields computation, numerical methods (such as Finite Element
Method (FEM), Finite Integration Technique (FIT) [1-3] and etc.) have been applied. For the time-
domain integration solution, explicit and implicit schemas have been widely used.
In comparison with implicit methods, the explicit methods are easier to realize in terms of
computation complexity, however, they are constrained by the stability condition. This condition
may require a small time step and therefore a prohibitive computing time. Another possibility is to
use an implicit schema which ensures the numerical stability. Unfortunately the implicit methods
require equation solved at each time step [4]. As a consequence, despite of a free choice on time
step, the computation time using the full implicit methods increases.
In this paper, fixed-point explicit calculation is introduced to an implicit schema. This method
combines the two advantages of implicit and explicit methods: no stability condition and no
equation solving. The solver is then applied to a time-domain eddy current problem. Using
orthogonal mesh cells and FIT, the mass-matrices in discrete formulations are diagonal. The fixed-
point explicit method allows direct calculations without matrix inversion or decomposition. |
[43] Comparison of Residual and Equilibrated Error Estimators for FEM Applied to Magnetostatic Problems COMPUMAG 2011 Sydney, Australie, 07/2011, Abstract TANG Zuqi, LE MENACH Yvonnick, CREUSE Emmanuel, NICAISE Serge, PIRIOU Francis |
In finite element computations, the choice of the mesh is crucial to obtain an accurate solution. In order to evaluate
the quality of the mesh, a posteriori error estimators can be used. In this paper, we analyze and compare the residual and equilibrated error estimators for magnetostatic problems. |
ACN Conférence nationale avec acte |
[1] Modélisation des effets capacitifs-inductifs couplés avec le modèle de Darwin SGE2023 (Lille), 07/2023 TAHA Houssein, TANG Zuqi, HENNERON Thomas, LE MENACH Yvonnick, SALOMEZ Florentin, DUCREUX Jean-Pierre |
[2] Caractérisation mécanique non destructive des aciers martensitiques par analyse du bruit Barkhausen SGE 2023, Lille, France, 07/2023, URL DHERBÉCOURT Marwane, MESSAL Oualid, TANG Zuqi, BENABOU Abdelkader, QOZAM Hanae, LEFEVRE Fabien, PETIT Sébastien |
[3] Computer-Aided Measurement method of Hysteresis Loop based on Convolution Neural Network SGE 2021, Nantes, France, 07/2021, Abstract GONG Ruohan, BENABOU Abdelkader, TANG Zuqi |
In this paper, a surrogate model base on deep learning (DL) is proposed to predict the hysteresis loops of ferro-magnetic materials. The databases of hysteresis loops were measured on the MPG200D Brockhaus equipment with an Epsteinframe. In order to reduce the experimental cost and accelerate measurements, a surrogate model based on the convolutional neural network (CNN) is proposed. First, presenting the measurement results in the form of 256× 256 × 1 images and extract the 6 most characteristic parameters, namely peak magnetic flux density, frequency, maximum magnetic field strength, remanence, coercivity, and the area of the hysteresis loop. All these physical parameters are taken as the label in the supervised DL process. These labe linformation are normalized to form a Gaussian distribution image of 256× 256 × 3 as the input, and the corresponding B-H curve is the output. Using image-to-image CNN U-net, once the network is effectively trained, the hysteresis loops under other excitation parameters can be predicted without further measurement. Our numerical examples show that the prediction results agree well with the measurement results. The sensitivity of CNN for hysteresis loops prediction with respect to the hyperparameters are investagted. A set of empirical hyperparameter configurations isput forward to guarantee an efficient convergence. This research shows that the proposed approach can be an efficient tool to predict the hysteresis loop of ferromagnetic materials under different circumstances, which can potentially contribute to nonlinear hysteresis FEM computation. |
[4] Estimateurs d’erreur a posteriori pour les équations de la magnétodynamique en formulation potentielle (A/φ) harmonique Journées du GDR Calcul 2011 Paris, 07/2011 TANG Zuqi |
HDR Habilitation à diriger des recherches |
[1] Contribution au développement numérique pour le calcul des champs électromagnétiques : étude du modèle de Darwin et investigation au Deep Learning Habilitation à diriger des recherches en génie électrique, Université de Lille, 04/2023 TANG Zuqi |
INV Conférence invité |
[1] Some Development of Numerical Tools for Darwin Model 19th International IGTE Symposium 2020, 20 - 23 September 2020 Graz, Austria, 09/2020 TANG Zuqi |
[2] Residual-based Error Estimator for Finite Element Method Applied to Quasi Static fields monag, Curitiba, 09/2014 LE MENACH Yvonnick, TANG Zuqi, TITTARELLI Roberta |
TH Thèse |
[1] Estimateurs d’erreur a posteriori résiduels en éléments finis pour la résolution de problèmes d'électromagnétisme en formulations potentielles Université Lille 1, 11/2012, URL, Abstract TANG Zuqi |
Résumé
Ce travail s’intéresse à la résolution numérique par éléments finis des équations de Maxwell en régime quasi-stationnaire et en formulations potentielles. L’objectif poursuivi consiste à développer des estimateurs d’erreur a posteriori résiduels, afin de contrôler l’erreur de discrétisation spatiale, dans le cadre d’applications en régime statique ou en régime dynamique harmonique.La première partie de cette thèse est composée de deux chapitres. Le premier est consacré à la modélisation des phénomènes physiques étudiés et à l’obtention des équations mathématiques en résultant. Dans le second, on présente les estimateurs a posteriori et leur intérêt dans le cadre de la mise en oeuvre de la méthode des éléments finis. On détaille notamment les notions de fiablité et d’efficacité d’un estimateur. La deuxième partie se décompose en trois chapitres. Le premier développe l’estimateur a posteriori dans le cas de la magnétostatique en formulation potentielle vecteur A. Les outils mathématiques nécessaires à l’étude sont en particulier détaillés. L’estimateur obtenu est alors validé sur quelques cas tests académiques. Le deuxième traite de l’estimateur a posteriori pour la formulation magnétodynamique en potentiel A/φ en régime harmonique. Un soin particulier est apporté pour générer une décomposition de Helmholtz ad hoc permettant d’obtenir la fiabilité de l’estimateur. Plusieurs configurations sont traitées en fonction de la position du domaine conducteur dans le domaine de calcul et des conditions aux limites associées. Un test numérique est ensuite effectué. Le troisième chapitre est consacré à l’estimateur d’erreur a posteriori pour la formulation T/Ω en régime harmonique pour le problème de la magnétodynamique, en supposant le domaine conducteur simplement connexe. Similairement à la formulation A/φ, une décomposition de Helmholtz est développée pour établir la fiabilité. Une validation numérique est proposée. Enfin, la troisième partie présente une batterie de tests numériques applicatifs et industriels permettant de tester les estimateurs développés dans des conditions réelles. Celle-ci se termine notamment par une application de EDF R&D ayant pour objet le contrôle non destructif par courant de Foucault de tubes générateurs de vapeur.
abstract
We are interested in resolving the Maxwell equations in the case of quasi-stationary and potential formulations when the finite element method is used. The aim of this work is to develop residual-based a posteriori estimators to control the spatial discretization error in magnetostatic and magnetodynamic problems. The first part is decomposed in two chapters. In the first one, the modeling of the physical phenomena involved are proposed and the mathematical equations are derived. Then, in the second one, the definition of the a posteriori estimators and their interest are presented in the context of the finite element method. The particular notions of reliability and efficiency of an estimator are presented. The second part can be decomposed into three chapters. In the first one, a residualbased a posteriori estimator for the vector potential formulation A in the case of magnetostatic problems is developed. Some necessary mathematical tools for the study are particularly detailed. The estimator is then validated by some academic tests. In the second chapter, a residual-based a posteriori estimator for the A/φ magnetodynamic harmonic formulation is developed. An ad-hoc Helmholtz decomposition is derived to obtain the reliability of the estimator. Several configurations are considered according to the position of the conductor domain in the computational domain as well as boundary conditions used. A numerical test is then performed. In the third chapter, a residual-based a posteriori estimator is derived for the T/Ω magnetodynamic harmonic formulation, when the conductor domain is simply connected. Similarly to the A/φ formulation, an ad-hoc Helmholtz decomposition is developed to establish the reliability. A numerical validation is proposed.Finally, in the third part, a set of numerical experiments and industrial applications are presented to evaluate our estimators. It ends with a particular application of EDF R&D focusing on the eddy current non-destructive evaluation of steam generator tubes. |
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