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The impedance boundary condition is widely used in order to reduce a multiple region electromagnetic field problem to a magnetic field problem analyzed in a nonconducting region only. It is obvious that the solution to the latter problem is much easier to obtain than those for conducting regions. There are several versions of the impedance boundary condition formulation which depend mainly on the choice of a field state variable and the solution technique applied.

Lorentz force evaluation is a non-destructive evaluation method for conducting specimens. The movement of a specimen relative to a permanent magnet leads to Lorentz forces that are perturbed in the presence of a defect. This defect response signal (DRS) is used for defect reconstruction. To solve a linear inverse problem for defect reconstruction, an accurate and fast forward computation method is required. As existing forward methods are either too slow or too inaccurate, the purpose of this paper is to propose the single voxel approach (SVA) as a novel method.

In SVA, the DRS is computed as a superposition of DRSs from single defect voxels, which are calculated in advance, by applying the boundary element source method. This research uses a setup of an isotropic conducting specimen, a spherical permanent magnet and defects of different shapes at different depths. With the help of simulations, this study compares the SVA to the previously proposed approximate forward solution (AFS) and the extended area approach (EAA) using the normalized root mean square error (NRMSE). Simulated data using the finite element method serve as the reference solution.

SVA shows across all simulations NRMSE values <2.5 per cent compared to <8 per cent for EAA and <12 per cent for AFS.

The superposition principle of SVA allows for the application of linear inverse methods for defect reconstruction while providing sufficient accuracy of the forward method.

We applied minimum norm estimations using different regularization techniques to the solution of the biomagnetic inverse field problem. Using magnetic field data measured with a multi‐channel‐SQUID‐sensor‐system we computed reconstruction of the impressed current density distributions which were generated by extended current sources placed inside a human torso phantom. The common inverse techniques usually applied in modern biomedical investigations in bioelectricity or biomagnetism are compared, and their aptitude for reconstruction of 3D current sources in space was evaluated. We analyzed the impact of using magnetic data, electrical data, and combination of both respectively on the localization of an equivalent current dipole (ECD). Finally, we use a visualization tool which enables a comparison of current density reconstruction. The study is, in parts, related to the new TEAM problem No. 31.

The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can be applied for the detection and reconstruction of defects lying deep inside a non-magnetic conducting material.

In this paper the technique is described in general as well as its experimental realization. Besides that, numerical simulations are performed and compared to experimental data. Using the output data of measurements and simulations, an inverse calculation is performed in order to reconstruct the geometry of a defect by means of sophisticated optimization algorithms.

The results show that measurement data and numerical simulations are in a good agreement. The applied inverse calculation methods allow to reconstruct the dimensions of the defect in a suitable accuracy.

LET overcomes the frequency dependent skin-depth of traditional eddy current testing due to the use of permanent magnets and low to moderate magnetic Reynolds numbers (0.1-1). This facilitates the possibility to detect subsurface defects in conductive materials.

Investigations which have been carried out up to the present have shown that trajectories of the arc spot over the extinguishing plate drift always towards the plate axis. Results of calculations presented in this paper are different from the results which have been obtained till now. The calculations have been made with the use of computer programs based on the boundary element method. The results of the calculations show that for some areas of plates of specific shapes potential gradient of a field of forces acting against the arc spot may approach zero. When the arc reaches any point of such an area it is stopped and the arc spot trajectory does not end at the plate axis.

The purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of a permanent magnet. The stress tensor allows for a transition from a volume to a surface integral for force calculation.

This paper derives a new stress tensor which consists of two parts: the first part corresponds to the scaled Poynting vector and the second part corresponds to the velocity term. This paper converts the triple integral over the volume of the conductor to a double integral over its surface, where the subintegral functions are continuous through the different compartments of the model. Numerical results and comparison to the standard volume discretization using the finite element method are given.

This paper evaluated the performance of the new stress tensor computation on a thick and thin cuboid, a thin disk, a sphere and a thin cuboid containing a surface defect. The integrals are valid for any geometry of the specimen and the position and orientation of the magnet. The normalized root mean square errors are below 0.26% with respect to a reference finite element solution applying volume integration.

Tensor elements are continuous throughout the model, allowing integration directly over the conductor surface.

In many different engineering fields often there is a need to protect regions from electromagnetic interference. According to static and low-frequency magnetic fields the common strategy bases on using a shield made of conductive or ferromagnetic material. Another screening technique uses solenoids that generate an opposite magnetic field to the external one. The purpose of this paper is to discuss the shielding effect for a magnetic and conducting cylindrical screen rotating in an external static magnetic field.

The magnetic flux density is expressed in terms of the magnetic vector potential. Applying the separation of variables method analytical solutions are obtained for an infinitely long magnetic conducting cylindrical screen rotating in a uniform static transverse magnetic field.

Analytical formulas of the shielding factor for a cylindrical screen of arbitrary conductivity and magnetic permeability are given. A magnetic Reynolds number is found to be an appropriate indication of the change in magnetic field inside the screen. Useful simplified expressions are presented.

This paper treats in a qualitative way the possibility of static magnetic field shielding by using rotating conducting magnetic cylindrical screens. Analytical solutions are given. If the angular velocity is equal to zero or the relative permeability of the shield is equal to one the shielding factor has forms well known from literature.

The purpose of this paper is to present the methodology of designing an exciter for Magnetic Induction Tomography (MIT). The design of the exciter must satisfy the following requirements: maximize MIT system sensitivity and minimize harmful influence on electronic MIT equipment.

Two objective functions are considered, namely: a magnetic flux density in the protected regions and a module of the eddy‐current density vector in the object under test in the vicinity of a sensor. The paper shows a multi‐objective optimization technique (based on the weighted sum method) which, by coupling the finite‐element method with a genetic algorithm, supports the design of the exciter.

It is possible to design in a relatively simple way an exciter for MIT under the given assumptions.

Detailed description of the multi‐objective optimization procedure has been presented.

The paper presents the features of an interactive “cube lens” approach to overcome some problems of visualization of 3D scalar or vector magnetic field. The “cube lens” is defined as a cubic part of the space where the 3D field is calculated using any method. The field data are given over a regular cubic grid. Several methods of scalar and vector fields visualization are presented.

This paper describes numerical tests for a three dimensional infinite element suitable for finite element modelling of open boundary field problems. The infinite element has four nodes and is compatible with conventional cuboids. The effectiveness of the infinite element in the interior — finite element region is shown by comparing the accuracy and the CPU time when various boundary conditions are applied. The possibility of computing the external fields is also illustrated.