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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.