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The LF magnetic field (50 Hz‐100 kHz) generated in the air by electrical appliances is characterised using multipoles. The maximum likelihood estimation of an equivalent multipolar source is computed using a genetic algorithm. The choice of the position and the number of measurement points are discussed.

The electromagnetic fields have a great influence on the behaviour of all the living systems. The as low as reasonably achievable (ALARA) principle imposes, in case of long exposures to low (i.e. power systems) or high frequency (i.e. microwave systems or cell phones) fields, some limitations to the radiated fields by the industrial equipment. On the other hand, some benefits can be taken from the effects of the electromagnetic fields on the living being: the hyperthermal technique is well known for the treatment of the cancer. Either we want to be protected from the fields, or we want to take benefit of the positive effects of these fields, all the effects thermal as well as genetic have to be well known. Like in any industrial application, the electromagnetic field computation allows a better knowledge of the phenomena, and an optimised design. Hence, there is a very important challenge for the techniques of computation of electromagnetic fields. The major difficulties that appear are: (1) related to the material properties – the “material” (the human body) has very unusual properties (magnetic permeability, electric permittivity, electric conductivity), these properties are not well known and depend on the activity of the person, and this material is an active material at the cell scale; (2) related to the coupling phenomena – the problem is actually a coupled problem: the thermal effect is one of the major effects and it is affected by the blood circulation; (3) related to the geometry – the geometry is complex and one has to take into account the environment. The problems that we have to face with are – the identification of the properties of the “material”, the coupled problem solution and the representation of the simulated phenomena.

In the ideal crack model (negligible thickness and an impenetrable barrier to electric current) in eddy‐current testing frame, the field‐flaw is equivalent to a current dipole layer on its surface. This dipole density is the solution of an integral equation with a hyperstrong kernel. This model has shown its efficiency, as well the computing accuracy, as for the CPU time. Furthermore, the case of a current leakage across crack was considered by introducing an equivalent conductivity of the crack. This paper aims at simulating a local varying conductivity. In particular, we focus on a constant piecewise conductivity. In this last case, because of the presence of the hypersingular kernel in the equation, the numerical scheme using the ideal case has to be modified.

For thin cracks, in eddy current testing (ECT), the field‐flaw interaction is equivalent to a current dipole layer on its surface. The dipole density is the solution of an integral equation with a hyperstrong kernel. The variation of coil impedance and eddy current distribution is directly obtained from this density by a surface integration. There is a numerical difficulty to evaluate accurately integrals for the current density near the crack. In fact, due to the singular kernel of a dyadic Green function, the integration is quasi‐singular. A specific regularisation algorithm is developed to overcome this problem and applied to represent eddy current distribution between two cracks.

The classical ϕ‐a formulations for numerical dosimetry of currents induced by extremely low frequency magnetic fields requires that the source field is provided through a vector potential. The purpose of this paper is to present a new formulation t‐b which directly takes the flux density as source term.

This formulation is implemented through finite element and validated by comparison with analytical solutions. The results obtained by both formulations are compared in the case of an anatomical computational phantom exposed to a vertical uniform field.

A good agreement between the t‐b formulation and both numerical and analytical computations was found.

This new formulation seems to be more accurate than the ϕ‐a formulation, and is more suited for situations where the magnetic field is known from experimental measurements, as there is no need for a magnetic vector potential.

This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures.

The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition.

It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results.

An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

A 3‐D eddy current code, TRIFOU, has been used to simulate eddy currents flowing around cracks in very thick conductors, which is a fully 3‐D situation. The measurement set and the probe have also been simulated so that we can compare numerical and experimental output signals. Storage and CPU‐time requirements are detailed and the expectations of such a program in non‐destructive testing are discussed.

The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM) technique with an extraction based on the Gauss‐Newton algorithm with Tikhonov regularization is applied.

The aim is to have a computationally fast recognition procedure of defects since the monitoring results in a large amount of data points that need to be analyzed by 3D eddy current model. According to the SM optimization, the finite element method (FEM) is used as a fine model, while the model based on an integral method such as the volume integral method (VIM) serves as a coarse model. This approach, being an example of a two‐level optimization method, allows shifting the optimization load from a time consuming and accurate model to the less precise but faster coarse surrogate.

The application of this method enables shortening of the evaluation time that is required to provide the proper parameter estimation of surface defects.

In this work only the specific kinds of surface defects were considered. Therefore, the reconstruction of arbitrary shapes of defects when using real measurement data from ECT system can be treated in further research.

The paper investigated the eddy current inverse problem. According to aggressive space mapping method, a suitable coarse model is needed. In this case, for the purpose of 3D defect reconstruction, the reduced VIM approach was applied. From a practical view point, the authors demonstrated that the two‐level inversion procedures allow saving of up to 50 percent CPU time in comparison with the optimization by means of regularized Gauss‐Newton algorithm in the same FE model.

The purpose of this paper is to describe the development of simulation tools dedicated to eddy current non destructive testing (ECNDT) on planar structures implying planar defects. Two integral approaches using the Green dyadic formalism are considered.

The surface integral model (SIM) is dedicated to ideal cracks, whereas the volume integral method is adapted to general volumetric defects.

The authors observed that SIM provides satisfactory results, except in some critical transmitting/receiving (T/R) configurations. This led us to propose a hybrid method based on the combination of the two previous ones.

This method enables to simulate ECNDT on planar structures implying defects with a small opening using T/R probes.

Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or direct contact to potential drops using the finite integration technique (FIT).

The methodology of calculating low‐frequency electromagnetic fields within high‐resolution anatomy models using the FIT is extended by a local grid refinement scheme using a non‐matching‐grid formulation domain. Furthermore, distributed computing techniques are presented. Several numerical examples are analyzed using these techniques.

Numerical simulations of low‐frequency current density distributions may now be performed with a higher accuracy due to an increased local grid resolution in the areas of interest in the human body voxel models when using the presented techniques.

The local subgridding approach is introduced to reduce the number of unknowns in the very large‐scale linear algebraic systems of equations that have to be solved and thus to reduce the required computational time and memory resources. The use of distributed computation techniques such as, e.g. the use of a parallel solver package as PETSc follows the same goals.