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Low frequency eddy current technique is being widely used for the nondestructive testing of metal objects. Computer simulation for eddy current nondestructive testing of metal objects is described in this paper.

The geometric properties of finite element mesh are of great importance. The refinement algorithm leads often to very irregular elements. The problem of optimization of 3D‐meshes is unsolved at this time. Only fragmentary methods are known. This paper presents a new concept of optimization algorithm and compares three different strategies for subdivision of tetrahedral elements.

The purpose of this paper is to present sensitivity analysis of electromagnetic fields in the time‐domain.

The method utilizing adjoint models is commonly used to evaluate sensitivity. In connection with widely applied finite element method, the time‐stepping scheme for discretization of time functions is used.

The proposed semi‐discrete method allows us to obtain time‐domain solution without time‐stepping. For space discretization, the authors use finite elements, as usual. The semi‐discrete method delivers analytical and continuous solution for any given time of analysis, which has a form of exponential functions. In order to obtain an analytical formula, there is necessary the integration of sensitivity equation. The paper finds possible solutions of this problem, either the application of Zassenhaus formula or improvement of commutation properties of two matrices.

Drawback of this method is matrices which are losing their symmetry and are no more banded. All calculations in this work were carried out with fully assigned matrices. Comparison of the efficiency of the semi‐discrete method with classical method shows that, despite the high demand for memory, this method can compete in relation to finite elements with the time‐stepping.

The resultant gradient information may be used for solving inverse problems, such as optimization of magnetic circuits and identification of material conductivity distributions.

The paper offers compact formula for sensitivity evaluation.

The sensitivity analysis determines the influence of geometrical or physical parameters on some global or local quantities, used as objective function. Two different methods for nodal and global sensitivity evaluation are discussed. A very efficient method of direct differentiation is proposed which enables calculation of energy functional perturbation caused by the nodal position movement. Otherwise, the optimal nodal position minimizing the energetic functional can be obtained. The second method, based on stiffness matrix inversion, is well known from circuit theory. It was adapted for computing the sensitivity of nodal potentials in finite elements to perturbations in chosen parameter of analyzed model. After the stiffness matrix has been inverted we obtain the new solution of the FEM problem and the sensitivity values of all nodal potentials of our model. This sensitivity can be easily computed versus many parameters, for example versus electrical conductivity in different elements. Such an approach allows us to identify conductivity variations, e.g. cracks in metals. To identify the crack shape and its conductivity, the iterative process is necessary. The desired data, as magnetic flux density, come from measurement. For the aim of test cases in this work, the measurement was simulated by finite element computation. On the surface of the conducting plate, cracks of different shape and conductivity were inserted. The models with cracks were analyzed with the FEM providing training data for further iterative process. Then the cracks were removed, and the algorithm tried to reconstruct the conductivity distribution based on sensitivity values of the nodes.

Describes the algorithm allowing recognition of cracks and flaws placed on the surface of conducting plate. The algorithm is based on sensitivity analysis in finite elements, which determines the influence of geometrical parameters on some local quantities, used as objective function. The methods are similar to that of circuit analysis, based on differentiation of stiffness matrix. The algorithm works iteratively using gradient method. The information on the gradient of the goal function provides the sensitivity analysis. The sensitivity algorithm allows us to calculate the sensitivity versus x and y, so the nodes can be properly displaced, modeling complicated shapes of defects. The examples show that sensitivity analysis applied for recognition of cracks and flaws provides very good results, even for complicated shape of the flaw.

The field of magnetic levitation by ferromagnetic attraction in conjunction with a linear propulsion system has experienced interest for many years. The increasing capacity of modern computers allow the use of numerical field calculation methods under very realistic conditions. This paper deals with possibilities of a scalar potential magnetic field analysis in a short‐stator propulsion system. The eddy currents in the railway were modelled by the special boundary condition for a thin sheet. The numerical algorithm is based on a finite element method with tetrahedrons. To increase the accuracy of calculations the adaptive technique was introduced. As results the calculated forces, power losses in the railway and the adaptive meshes were shown.

This paper aims to present effective methods for computing electromagnetic field sensitivity in the time domain versus conductivity perturbations in finite elements.

Two‐dimensional cases in linear, isotropic media are considered and two effective methods for sensitivity analysis of a magnetic vector potential in the time domain are described.

The paper finds that the convergence of numerical identification algorithm depends on exact measurement of magnetic flux density. For identification of real cracks the application of data filtering and TSVD regularization of Gauss‐Newton algorithm is necessary.

The resultant gradient information may be used for solving inverse problems such as the identification of material conductivity distributions.

The algorithms described are based on known methods from established circuit theory – incremental circuit and adjoint circuit, these have been expanded to apply in electromagnetic field theory.

This paper presents the practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation is proposed using Helmholtz's equation and Biot‐ Savart's law. The system equation is solved by using the finite element method (FEM). The exemplary results of calculation ‐ eddy currents lines in material and relative resistance versus probe position are presented.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.