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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.

A method, which is using the electric vector potential T and the magnetic scalar potential Ω is presented for the calculation of the electro‐magnetic field inside conducting cylinders of infinite length.The current source is an oscillating current dipole arbitrarilly oriented. The Green's function method is used for the transformation of the Helmholtz's equations for T and Ω into integral ones. Finally a boundary element technique is used to obtain a system of simultaneous equations. In this system the number of the unknows is greater than the number of the availiable simultaneous equations.Thus some additional conditions between the field quantities, have to be added to the boundary conditions to obtain the final solution of the problem. Problems of electrical machines, electromagnetic shielding or even, problems related to human bodies can be treated with the following analysis.

The application of the equivalent source methods for the numerical calculation of the total magnetic force acting upon a permanent magnet is proposed. These methods are formulated in terms of the external field, which allows the complete avoidance of the numerical inaccuracies affecting force computation due to the singularity of the self‐field of the magnet on its edges. It is shown, with the help of some 2D and 3D test cases, that the proposed formulae provide reliable and stable results, even when the FEM mesh is not refined. Such results have also been compared with those derived from more traditional methods, such as the surface integration of the Maxwell’s stress tensor and the virtual work method, exhibiting better precision and lower computational costs.

The resolution of electroencephalography (EEG) forward problem by the finite element method (FEM) involves the modeling of current dipoles with the singularities. The purpose of the paper is to investigate the accuracy issue of the two alternative methods, the direct method and the subtraction method for the modeling of current dipoles.

Finite element modeling of current dipoles using the direct method and the alternative implementations of the subtraction method.

The accuracy and the performance of different methods are compared through a four-layer spherical head model with available analytical solution. Results show that the subtraction method involving only the surface integrals provides the best accuracy.

The subtraction method removes the difficulty of modeling the singularity of current dipoles but the accuracy depends on the implementation.

An appropriate equivalent model is the key to the effective analysis of the system and structure in which permanent magnet takes part. At present, there are several equivalent models for calculating the interacting magnetic force between permanent magnets including magnetizing current, magnetic charge and magnetic dipole–dipole model. How to choose the most appropriate and efficient model still needs further discussion.

This paper chooses cuboid, cylindrical and spherical permanent magnets as calculating objects to investigate the detailed calculation procedures based on three equivalent models, magnetizing current, magnetic charge and magnetic dipole–dipole model. By comparing the accuracies of those models with experiment measurement, the applicability of three equivalent models for describing permanent magnets with different shapes is analyzed.

Similar calculation accuracies of the equivalent magnetizing current model and magnetic charge model are verified by comparison between simulation and experiment results. However, the magnetic dipole–dipole model can only accurately calculate for spherical magnet instead of other nonellipsoid magnets, because dipole model cannot describe the specific characteristics of magnet's shape, only sphere can be treated as the topological form of a dipole, namely a filled dot.

This work provides reference basis for choosing a proper model to calculate magnetic force in the design of electromechanical structures with permanent magnets. The applicability of different equivalent models describing permanent magnets with different shapes is discussed and the equivalence between the models is also analyzed.

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.

Applies four different minimum norm estimations with common regularization techniques, often used in biomedical applications to the solution of the biomagnetic inverse field problem. Magnetic field data measured with a multi‐channel biomagnetometer sensor system in a magnetically shielded room were used to reconstruct the current density distributions generated by an extended current source which was placed inside a human torso phantom. No one of the tested methods is able to estimate the extension of the source. To improve the results as much as possible a priori information of the source space should be taken into account.

The electroencephalography (EEG) source tomography in bio‐electromagnetics is to estimate current dipole sources inside the brain from the measured electric potential distribution on the scalp surface. A traditional algorithm is the low‐resolution electromagnetic tomography algorithm (LORETA). In order to obtain high‐resolution tomography, the LORETA‐contracting algorithm is proposed.

The relation between the dipolar current source J at the nodes in source region and the potential U at the observed points on the scalp surface can be expressed as a matrix equation U=KJ after discretization. K is a coefficient matrix. Usually its simultaneous equation is an under‐determined system. The LORETA approach is to find out min‖BWJ‖², under constraint U=KJ where B is the discrete Laplacian operator matrix, W is a weighting diagonal matrix. Its solution is J=(WB^TBW)⁻¹K^T{K(WB^TBW)⁻¹K^T}⁺U where {}⁺ denotes the Moore‐Penrose pseudo‐inverse matrix. The improvement on this approach is to establish an iterative program to repeat LORETA and reduce the number of unknown J quantities in the step i+1 by contracting the source region excluding some extreme little quantities of J given in the step i. The simultaneous equations will gradually turn to a properly determined system or to an over‐determined system. Finally, its solution can be obtained by using the least square method.

Repeating to make the low‐resolution tomography by contracting the source region, we can get a high‐resolution tomography easily.

The LORETA‐contracting algorithm is based on the assumption that the dipolar current sources inside the brain are sparse and concentrated based on the physiological study of the brain activity.

It is new to repeat LORETA combined with the contracting technique. This algorithm can be developed to solve EEG problems of realistic head models.

The purpose of this paper is to present a novel eddy-current modeling technique of volumetric defects embedded in conducting plates. This problem is of great interest in electromagnetic non-destructive evaluation and has already been exhaustively studied.

The defect is modeled by a volumetric current dipole density which satisfies an integral equation. The latter is solved by the classical method of moments. The authors propose the use of globally defined, continuous basis functions for the expansion of the current dipole density.

The proposed global expansion provides an improvement of the numerical stability and the performance of the simulation, over classical approaches. The proposed method is tested against both measured and synthetic data obtained by a different defect model.

The new discretisation scheme – in contrast to the classical approaches – does not need the discretisation of the defect volume. This involves numerous advantages that are discussed in the paper.

The purpose of this paper is to develop a source reconstruction technique, applied to a case study in biomagnetism, using both evolutionary optimization and regularization techniques.

The magnetic field, produced by a current dipole in a spheroidal domain modeling the head, is calculated. Although the model is very simple, the magnetic effect of a brain source is appropriately simulated. In order to solve the source identification problem, the following approaches have been implemented: a single‐objective minimization of a residual function, based on an evolutionary algorithm, is applied first; then, the L‐curve criterion for regularization is implemented by means of an iterative search.

A variable number of unknown parameters, defining direction and magnitude of the current dipole, have been considered. As a consequence, several optimization problems are solved: a technique based on the use of the lead field matrix identifies the source with the smallest error. Eventually, an iterative procedure based on Tikhonov regularization is proposed. The algorithm is tested with and without noise affecting data. The results showed an accuracy comparable to that obtained independently with the optimization approach.

A model problem in inverse biomagnetism, which is both simple and significant, has been formulated and solved. The magnetic source of brain activity is reconstructed in a fast way and with small errors by means of two techniques of field inversion.