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We propose a recipe to construct a symmetric positive definite and consistent reluctance constitutive matrix to be used within discrete geometric approaches when the primal grid is generated by an enhanced subgridding of a generic hexahedral grid. We focus on a magnetostatic problem as working example. Index Terms--Cell method, discrete constitutive relations, magnetostatics, subgridding.

In this paper, we formulate an electroquasistatic problem according to the discrete geometric approach. As an application, the transient behavior of the gas insulated transmission line for the ITER neutral beam injector system is analyzed. Index Terms--Cell's method, discrete geometric approach, electroquasistatics, FIT, high voltage applications, ITER, NBI.

The analysis of a microelectrostatic actuator is presented, formulated by means of the so-called Discrete Geometric Approach applied to the solution of the electrostatic-elastostatic coupled problem. Numerical results computed by means of the proposed approach are compared to those coming from assessed approaches like the finite-element method (FEM) (for both the structural and the electric domains) and FEM/boundary element method (BEM) (FEM for the structure, BEM for the electric domain). A preliminary experimental validation is finally added. Index Terms--Discrete geometric approach, finite elements, microelectromechanical systems (MEMS).

We present an inversion procedure for the image reconstruction of defects in metallic plates, using a multifrequency eddy-current system. The solution of the eddy-current forward problem is achieved by means of a discrete geometric approach, while the inverse problem is resolved with an iterative linearization algorithm based on sensitivity data. In particular, we propose a suitable measurement point on the region under test using a probe coil exited by means a multifrequency signal, in order to improve the amount of usable data and the accuracy of the inverse procedure. Index Terms--Discrete geometric approach, inverse problems, multifrequency eddy currents, sensitivity analysis.

We propose a way to couple field equations for quasistatics in a bounded domain--where electromagnetic phenomena are assumed to be confined--with circuit equations. The algebraic equations describing eddy-current problems are obtained by means of a discrete geometric formulation A-x, based on the circulation of the magnetic vector potential A and a scalar potential x. Index Terms--Coupled-problems, discrete approaches, eddy currents.

We propose a pair of discrete geometric formulations to model two-dimensional (2-D) photonic crystals. Photonic crystals are periodic materials able to guide light by Bragg's reflection. We compared the results with an independent approach based on the multiple-scattering technique (MST). Index Terms--Discrete approaches, photonic crystals, wave propagation.

In this paper, a time-domain formulation for two-dimensional (2-D) eddy-current problems based on a discrete geometric approach is presented. The method bears very strong similarities with a mass-lumped [theta]-type finite-element method (FEM) formulation. Analogies and differences are highlighted, and a numerical experiment is reported. Index Terms--Discrete approaches, eddy-currents, mass lumping, [theta]-method.

The finite-element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate to field problems on the discrete level. Although the finite-element technique is explained typically in terms of variational or weighted-residual approaches, another, less familiar way is available to introduce the same ideas geometrically. Using magnetostatics as an example, we will show how finite-element-type system matrices can be developed by exploiting the geometric properties of so-caned Whitney elements. The simple interpretation we gain thereby enables us to view also the convergence properties of finite-element-type schemes in an intuitive way. Index Terms--Cell method, convergence, differential geometry, dual meshes, finite-element method.

A theoretical and numerical analysis is described and discussed involving the performance of a magnetic field (MF) probe system for testing of International Thermonuclear Experimental Reactor (ITER)-type cables.

The paper deals with a method, based on the finite formulation approach for the solution of a quasi-static eddy-current problem (ECP). As an example, the method has been tested against a two-dimensional axisymmetric ECP and the obtained results have been compared with those from well-established methods. The finite formulation is a new formulation, complementary to the traditional differential formulation, consisting of a discrete, i.e., algebraic, formulation obtained directly from experimental facts, without applying a discretization procedure to a differential equation. It adopts the global variables together with the primal-dual cellulization of the space and time domain as starting point. Index Terms--Eddy currents, quasi-static magnetic field.

Condition number G is proposed as a quality index for the location of field probe signals during tests on superconducting cables.

A method for the computation of the induction field in presence of open and closed passive conductors has been developed. It solves uniquely the inverse problem to determine the eddy currents needed in the passive conductors to produce a given flux. The method has been applied to the case of the RFX experimental machine to reconstruct the induction field inside the vacuum vessel. Index terms-Inverse problems, eddy currents, circuit equation, quasi-static magnetic fields, fusion machines.

A benchmark for inverse problems in magnetostatics, characterized by four geometrical of design variables, is revisited; its solution is tackled by means of a quasi-analytical optimization methodology. A set of initial designs, generated in a random way, is considered; the study of the functional dependence of the optimization results on the starting configurations is investigated.

A method for the calculation of the currents in the poloidal field coils of a toroidal magnetic confinement machine, which produce an induction field with specified stability properties has been developed and implemented. A procedure based on this method is currently applied to adjust the power supplies of the PF coils during the experimental sessions of RFX. RFX is a toroidal machine based on the Reversed Field Pinch (RFP) concept and it has been operating in Padua since 1991.

The paper presents the results of the validation of the plasma contour identification code PLACID. This code has been developed to reconstruct the poloidal magnetic field configuration produced during the plasma pulses of the RFX machine. PLACID input data are the signals of electromagnetic probes measured during the machine pulses. A set of validation tests has been performed in order to check the accuracy of the procedure implemented in PLACID and its sensitivity to noise in data. Input data for PLACID code have been generated by means of a virtual machine which simulates the actual machine. The virtual magnetic field configurations have been compared with the corresponding reconstructed configurations.

The paper describes a method for the identification of the plasma shape in a toroidal device for fusion experiments based on magnetic confinement. The method, developed for the RFX machine, makes use of the magnetic measurements and takes into account the electromagnetic effects of a conductive vacuum vesse and of a stabilizing shell. These effects are quite important in 'fast' machine such as the RFPs of the present generation.

RFX is a magnetic confinement toroidal machine based on the Reversed Field Pinch (RFP) concept (1). It is in operation at the 'Istituto Gas Ionizzati' in Padua since a few months. A study of the magnetic configurations with null-field points (X-points) has been performed in order to analyze the feasibility of operating RFX with a magnetic divertor. A reasonable solution has been found by means of an optimization procedure, which takes into account both physical and technical requirements, such as uniform vertical field for equilibrium, plasma cross section, thermal and electrodynamical loads on the coils.