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This paper aims to present the use of magnetic gradient, and magnetic potential measurements in the specific case of magnetization identification for a thin sheet. Usually, induction measurements are only used.

After a brief description of the magnetic gradient and magnetic scalar potential notions, methods to calculate them are presented and validated. These two kinds of measurements are tested for a numerical identification case. Then, virtual measurements can be generated and used for inverse problem resolution. Advantages of using induction, magnetic gradient or magnetic potential measurements are then discussed.

A previous method to solve inverse problem based on induction measurement has been increased by the capability of using other kind of measurements. A numerical approach has allowed to validate the use of magnetic gradient or magnetic scalar potential measurement as information sources.

Usually, induction measurements are only used. Inversion resolution using other kind of measurements than the induction can be made. An experimental validation has been done for gradient measurements.

Thin conducting sheets are used in many electric and electronic devices. Solving numerically the eddy current problems in presence of these thin conductive sheets requires a very fine mesh which leads to a large system of equations, and it becomes more problematic in case of higher frequencies. The purpose of this paper is to show the numerical pertinence of equivalent models for 3D eddy current problems with a conductive thin layer of small thickness e based on the replacement of the thin layer by its mid-surface with equivalent transmission conditions that satisfy the shielding purpose, and by using an efficient discretization using the boundary element method (BEM) to reduce the computational work.

These models are solved numerically using the BEM and some numerical experiments are performed to assess the accuracy of the proposed models. The results are validated by comparison with an analytical solution and a numerical solution by the commercial software Comsol.

The error between the equivalent models and analytical and numerical solutions confirms the theoretical approach. In addition to this accuracy, the computational work is reduced by considering a discretization method that requires only a surface mesh.

Based on a hybrid formulation, the authors present briefly a formal derivation of impedance transmission conditions for 3D thin layers in eddy current problems where non-conductive materials are considered in the interior and the exterior domain of the sheet. BEM is adopted to discretize the problem as there is no need for volume discretization.

This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation.

Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed.

The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh.

The propagation effects are not taken into account in the proposed formulation.

The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

The purpose of this paper is to propose a compact model to represent the magnetic field outside the sources. This model provides the multipolar ordering of a spherical harmonic expansion far from the source while being valid in its close proximity.

The authors investigate equivalent surface sources that enable to compute the field very close to any chosen surface that encloses the source. Then the authors present a method to find an appropriate initial basis and its associated inner product that allow to construct multipolar harmonic bases for these equivalent sources, where any vector of order k produces a field that decreases at least as fast as the field produced by a multipole of order k. Finally, those bases are numerically implemented to demonstrate their performances, both far from the source and in its close proximity.

The charge distribution and normal dipole distribution are well-suited to construct multipolar harmonic bases of equivalent sources. These bases can be described by as few parameters as the decreasing spherical harmonic expansion. Comparison with other numerical models shows its ability to compute the field both far from the source and close to it.

A basis for normal dipole distribution has already been described in the literature. This paper presents a general method to construct a multipolar basis for equivalent sources and uses it to construct a basis for single-layer potential.

This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker.

Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W² in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W¹ in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W¹. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values.

With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W² and using edge elements in space W¹. When solving the inverse problem in space W¹, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred.

The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

The aim of this paper is to model time‐harmonic problems in unbounded domains with coils of complex geometry and ferromagnetic materials.

The approach takes the form of a coupling between two integrals methods: the magnetic moment method (MMM) and the partial element equivalent circuit (PEEC) method. The modeling of conductor system is achieved thanks to PEEC method while the MMM method is considered for the magnetic material.

The paper shows how to use the MMM/PEEC coupled method to model a problem comprising conductors and ferromagnetic materials and compare its results with the FEM and the FEM/PEEC coupling.

The two methods PEEC and MMM are well‐known. The innovation here is coupling these methods in order to take advantages from both methods. Moreover, the performances of this coupling are studied in comparison with others (FEM, FEM/PEEC coupling).

This paper deals with the problem of magnetization identification. We consider a ferromagnetic body placed in an inductor field. The goal of this work is, from static magnetic field measurements taken around the device, to obtain an accurate model of its magnetization. This inverse problem is usually ill‐posed and its solution is non‐unique. It is then necessary to use mathematical regularization. However, we prefer to transform it to a better posed one by incorporating our physical knowledge of the problem. Our approach is tested on the magnetization's identification of a real ferromagnetic sheet.

This paper aims to compute the magnetic stray field created by faulty electrical machines.

This paper proposes two approaches to compute the magnetic stray field created by faulty electrical machines. The first one presents a homogenized FEM method. The second one is based on a combination of an analytical expression for the magnetic field in the machine air gap with an integral method.

The studies show good agreement and demonstrate the reliability of the approach.

Two models developed in this paper originally used to compute the stray magnetic field of electrical machines. They can contribute to develop new tools for fault monitoring.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

The purpose of this paper is to show that constructing magnetic equivalent circuits (MECs) for simulating accelerator magnets is possible by defining a three-port magnetic element for modelling the T-shape field distribution, where the flux leaves the yoke and enters the aperture.

A linear three-port magnetic element is extracted from an analytical field solution and can be represented by a number of two-port elements. Its nonlinear counterpart is obtained as a combination of the corresponding nonlinear two-port elements. An improved nonlinear three-port element is developed on the basis of an embedded nonlinear one-dimensional finite element model.

The T-shaped field distribution comes together with a complicated interplay between the saturation of the ferromagnetic yoke parts and flux leaking to the aperture. This is more accurately modelled by the improved nonlinear three-port magnetic element.

MECs have a limited validity range, especially for configurations where a high saturation level and fringing flux effects coexist.

The results of the paper appeal to be careful with applying nonlinear MECs for simulating bending magnets.

A new nonlinear three-port magnetic element for ferromagnetic yoke parts with T-shaped flux distribution has been developed.