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We examine the construction of reluctivity and Ohm's constitutive matrices for discrete geometric approaches using nonregular hexahedra as primal volumes. The effect of element deformation on the representation of uniform fields have been investigated for static fields. Then convergence and accuracy of the proposed matrices has been carried out using an eddy-current problem as working example. Index Terms--Constitutive matrices, discrete geometric approaches, eddy-currents.

We propose a discrete geometric formulation based on a magnetic scalar potential and on the circulation of an electric vector potential to solve eddy-current problems for nondestructive evaluation of steel bars with longitudinal defects. Index Terms--Discrete formulations, eddy-currents, nondestructive evaluations.

We propose a geometric reinterpretation of the Nodal Force Method in the framework of a pair of discrete formulations for magnetostatics on complementary meshes. Index Terms--Discrete approaches, forces, magnetostatics.

We examine the construction of a symmetric positive definite conductance matrix for eddy-current problems, using a discrete approach. We construct a new set of piecewise uniform basis vector functions on both the primal and the dual complex. We define these vector functions for both tetrahedra and prisms. Index Terms--Cell method, constitutive matrices, discrete approaches, eddy currents.

Using a geometric formulation for eddy currents, we present a geometric approach to constructing approximations of the discrete magnetic and Ohm's constitutive matrices. In the case of Ohm's matrix, we also show how to make it symmetric. We compared the impact on the solution of the proposed Ohm's matrices, and an iterative technique to obtain a consistent right-hand-side term in the final system is described. Index Terms--Cell complexes, cell method, constitutive matrices, eddy currents.

An algebraic formulation has been developed for the solution of three-dimensional eddy current problems, according to the cell method philosophy. This formulation is presented in the frequency domain and it is based on the circulation of magnetic vector potential along primal edges and on time-integrated electric scalar potential in primal nodes of conducting region. The formulation has been applied to solve a nondestructive evaluation problem. The flaw has been modeled as a zero-thickness defect and the superposition of effects has been applied to compute the impedance variation with respect to the flawless configuration. Index Terms--Cell method, dual meshes, eddy currents, electromagnetic nondestructive evaluation (NDE).

The research in the thermonuclear fusion area has entered the design phase of ITER, the first experimental Tokamak reactor. In the ITER device, the plasma shape and position are controlled by an active system on the basis of a real-time estimate of the plasma magnetic boundary. This identification process must be prompt and accurate enough to satisfy the tight control requirements. In this paper, a brief discussion about the reconstruction of the plasma boundary by means of the 'equivalent currents' (EC) method, in presence of conducting structures, will be presented. Some hints about a possible way to include the differential equations describing the vessel eddy currents will be illustrated. Index Terms--Eddy currents, nuclear fusion, plasma identification.

The protection of the Windings of RFX against fast electric faults relies on an original dedicated Fast Protection System able to operate within 1 ms. The first ring of the protection chain is the fault protection system of the winding, named RGM, that consists of: about hundred highly reliable voltage and current probes, all electric signal lines and an analog-digital device where signals are processed and logic alarms are generated. RGM is an original machine that required a careful design and manufacturing work. After a long test and adjustment phase it now operates properly. It has already operated against some earth faults which, due to low level of earth current, were not dangerous for the machine but very hard to detect.

An electromagnetic wave propagation problem can be formulated according to a pair of complementary formulations, called the e -formulation and the h -formulation. The two formulations are linked to each other by Maxwell’s curl equations, and, in the continuous setting, they are perfectly equivalent in describing the wave propagation phenomenon. However, this is not true in the discrete setting, where the two formulations, in general, give different solutions. In the past decades, complementary formulations were widely studied for static problems and eddy-current problems, where they were exploited as error estimators for adaptive refinement schemes. Moreover, the so-called bilateral energy bounds arise for some problems whether theoretically or at least numerically. However, to the best of our knowledge, little attention has been given to complementarity in the wave propagation problems. In this paper, we propose an adaptive refinement scheme using the constitutive error as an estimator, and then, we investigate the behavior in terms of bilateral energy bounds. [ABSTRACT FROM AUTHOR]

The aim of the paper is to present an automatic and general technique, suitable with the A-X geometric eddy-current formulation, to impose sources over massive conductors of any shape. For this purpose, the localized source approach is used, which does not require the solutions of steady-state conduction problems in the preprocessing stage. Nevertheless, this approach needs a thick cut in each active conductor, which is usually found "by hand." In this paper, an automatic and general algorithm to compute such thick cuts is introduced. Some benchmark problems are presented to demonstrate the generality and the robustness of the algorithm. [ABSTRACT FROM AUTHOR]

A perturbation method for the T - Ω geometric formulation to solve eddy-current problems is introduced. The proposed formulation is applied to the feasibility design of a nondestructive evaluation device suitable to detect "long" longitudinal flaws in hot steel bars. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a 3-D time-domain eddy-current A formulation based on the discrete geometric approach (DGA) over unstructured and nonorthogonal hexahedral dual grids. The resulting differential algebraic system of equation, solved by means of a singly-diagonally implicit Runge-Kutta (SDIRK) variable step-size solver, leads to very accurate results at reduced computational costs, as shown by numerical analysis. [ABSTRACT FROM AUTHOR]

We propose a discrete geometric formulation based on a magnetic scalar potential and on the circulation of an electric vector potential to solve eddy-current problems for nondestructive evaluation of steel bars with longitudinal defects. [ABSTRACT FROM AUTHOR]

Using a geometric formulation for eddy currents, we present a geometric approach to constructing approximations of the discrete magnetic and Ohm's constitutive matrices. In the case of Ohm's matrix, we also show how to make it symmetric. We compared the impact on the solution of the proposed Ohm's matrices, and an iterative technique to obtain a consistent right-hand-side term in the final system is described. [ABSTRACT FROM AUTHOR]

Deals with a study which presented the solution of a three-dimensional magnetostatic problem using the finite formulation of an electromagnetic field. Background on finite formulation and space discretization; Constitutive equation; Magnetostatic formulations; Numerical experiments and discussion; Conclusion.

Deals with a study which applied the finite formulation method to the solution of plane electrostatic problems on triangular and quadrilateral primal mesh elements. Information on global variables in finite formulation; Electric constitutive equation; Numerical results and discussion; Conclusion.

Deals with the application of the Genetic Algorithms (GA) to solve the inverse problem of the synthesis of the magnetic configuration for Magnetic Resonance Imaging. Description of the Genetic Algorithms; Details on the synthesis problem; Results of the application of the GA; Sensitivity analysis; Conclusions.

Provides information on a study which examined a method for the identification of plasma magnetic contour in machines for fusion research using magnetic measurements. Description of the identification problem; Application and results; Conclusions.