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This paper first introduces a simplified construction of the constitutive matrices for general polyhedral meshes. These constitutive matrices are geometrically defined by means of simple closed-form expressions involving the geometric elements of the primal and dual meshes. Then, we solve for the first time the Maxwell’s eigenvalue problem on general polyhedral meshes. In particular, we analyze the convergence of the eigenvalues when the mesh is adaptively refined by using the subgridding technique together with the constitutive inconsistency as error indicator. [ABSTRACT FROM AUTHOR]

This paper presents a novel discrete model for cell membranes and electrodes contact impedances alternative to the widely used finite elements. The finite element approach can be considered as a tool for constructing finite dimensional systems of equations that approximate the specific electroquasistatic biological problem 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 reformulate geometrically the same physical problem. This approach, referred to as discrete geometric approach, allows a direct link between geometry and the degrees of freedom describing the specific biological problem. It is straightforward to implement in any finite element open software and it assures a correct modeling of voltages and currents playing a fundamental role in a biological problem. The validation has been performed, as a first step, against analytical solutions; then, we considered impedance measurements regarding erythrocytes in whole blood flowing in microchannels at high shear rates. [ABSTRACT FROM PUBLISHER]

Abstract: The time independent Schrödinger equation stems from quantum theory axioms as a partial differential equation. This work aims at providing a novel discrete geometric formulation of this equation in terms of integral variables associated with precise geometric elements of a pair of three-dimensional interlocked grids, one of them based on tetrahedra. We will deduce, in a purely geometric way, a computationally efficient discrete counterpart of the time independent Schrödinger equation in terms of a standard symmetric eigenvalue problem. Moreover boundary and interface conditions together with non homogeneity and anisotropy of the media involved are accounted for in a straightforward manner. This approach yields to a sensible computational advantage with respect to the finite element method, where a generalized eigenvalue problem has to be solved instead. Such a modeling tool can be used for analyzing a number of quantum phenomena in modern nano-structured devices, where the accounting of the real 3D geometry is a crucial issue. [ABSTRACT FROM AUTHOR]

Abstract: By exploiting the geometric structure behind Maxwell’s equations, the so called discrete geometric approach allows to translate the physical laws of electromagnetism into discrete relations, involving circulations and fluxes associated with the geometric elements of a pair of interlocked grids: the primal grid and the dual grid. To form a finite dimensional system of equations, discrete counterparts of the constitutive relations must be introduced in addition. They are referred to as constitutive matrices which must comply with precise properties (symmetry, positive definiteness, consistency) in order to guarantee the stability and consistency of the overall finite dimensional system of equations. The aim of this work is to introduce a general and efficient set of vector functions associated with the edges and faces of a polyhedral primal grids or of a dual grid obtained from the barycentric subdivision of the boundary of the primal grid; these vector functions comply with precise specifications which allow to construct stable and consistent discrete constitutive equations for the discrete geometric approach in the framework of an energetic method. [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]

As a first step, we will investigate the extent of the consistency error for a hexahedral primal grid due to the use mass matrices of finite elements within the discrete geometric approach (DGA) as discrete counterparts of the constitutive relations. Such matrices are constructed by resorting to mixed elements edge and face vector functions. Then, we will propose a novel set of geometric vector basis functions for hexahedra that guarantee consistency and stability of the constitutive matrices for the DGA constructed according to the so-called energetic approach. [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]

We propose a geometric reinterpretation of the Nodal Force Method in the framework of a pair of discrete formulations for magneto- statics on complementary meshes. [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]

We examine the construction of reluctivity and Ohm's constitutive matrices for discrete geometric approaches using nonregular hexa-hedra 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. [ABSTRACT FROM AUTHOR]