Ruben Specogna

A new set of basis functions for the discrete geometric approach

By exploiting the geometric structure behind Maxwells 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.

Symmetric Positive-Definite Constitutive Matrices for Discrete Eddy-Current Problems

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

Modeling of epoxy resin spacers for the 1 MV DC gas insulated line of ITER neutral beam injector system

The spacers for the gas insulated transmission line for the ITER neutral beam injector will be designed to withstand the operating voltage of 1 MV dc. Electric charging processes of the spacer surface are then expected to play an important role in the final electric field distribution. Aim of the paper is to investigate the effects of the different conductivity properties of the SF6-Spacer insulating structures on the surface charge set-up, and to identify a procedure to minimize this charge. Based on the most updated literature, the paper presents and discusses the results of two newly developed simulation tools: the first consisting of a quasi-static non linear model for epoxy spacer based on finite element method code ANSYStrade, the other consisting of a spacer profile optimization package, whose kernel is based on a genetic algorithm. The numerical tools have been applied to post and disk spacer models of the gas insulated line; in particular, the optimization package has been used on the disk spacer, and the comparison between un-optimized and optimized spacer in terms of electric charge accumulated are presented and discussed.

Discrete constitutive equations in A-/spl chi/ geometric eddy-current formulation

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

Extraction of VLSI Multiconductor Transmission Line Parameters by Complementarity

Solving lossy multiconductor transmission line (MTL) equations is of fundamental importance for the design and signal integrity verification of interconnections in VLSI systems. It is well established that the critical issue is the efficient and accurate electrical characterization of the MTLs through the determination of their per-unit-length parameters. In this respect, the so-called complementarity has the potential to become a fast and accurate method for the extraction of these parameters. Besides the value of the parameters, in fact, complementarity provides rigorous error bounds for them. Despite this important feature, commercial software do not use complementarity yet, due to the fact that there are unsolved theoretical issues related to the nonstandard formulation based on the electric vector potential. Some attempts to fill this gap have been already reported. The aim of this paper is to fill this gap by introducing a general formulation based on the electric vector potential highlighting the advantages of complementarity with respect to the standard first- and second-order finite element formulations.

Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

a b s t r a c t The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to competing ones, allowing to handle problems not addressable before. In particular, when generators are employed in the physical modeling of magneto-quasistatic problems, this algorithm solves one of the most long- lasting problems in low-frequency computational electromagnetics. In this case, the effectiveness of the algorithm and its ease of implementation may be even improved by introducing the novel concept of lazy cohomology generators.

Critical Analysis of the Spanning Tree Techniques

Two algorithms based upon a tree-cotree decomposition, called in this paper spanning tree technique (STT) and generalized spanning tree technique (GSTT), have been shown to be useful in computational electromagnetics. The aim of this paper is to give a rigorous description of the GSTT in terms of homology and cohomology theories, together with an analysis of its termination. In particular, the authors aim to show, by concrete counterexamples, that various problems related with both STT and GSTT algorithms exist. The counterexamples clearly demonstrate that the failure of STT and GSTT is not an exceptional event, but something that routinely occurs in practical applications.

Lazy Cohomology Generators: A Breakthrough in (Co)homology Computations for CEM

Computing the first cohomology group generators received great attention in computational electromagnetics as a theoretically sound and safe method to produce cuts required when eddy-current problems are solved with the magnetic scalar potential formulations. This paper exploits the novel concept of lazy cohomology generators and a fast and general algorithm to compute them. This graph-theoretic algorithm is much faster than all competing ones being the typical computational time in the order of seconds even with meshes formed by millions of elements. Moreover, this paper introduces the use of minimal boundary generators to ease human-based basis selection and to obtain representatives of generators with compact support. We are persuaded that this is the definitive solution to this long-standing problem.

Image Reconstruction of Defects in Metallic Plates Using a Multi-Frequency Detector System and a Discrete Geometric Approach

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 procedureThis work presents an inversion procedure for the image reconstruction of defects in metallic plates using eddy current testing. We performed a minimization technique based on a discrete geometric approach for eddy currents, and an iteration procedure driven by sensitivity data. In particular we propose a multi-probe detector system excited with multi-frequency signal, in order to increase the number of sensitivity data. In this way we improve the accuracy and efficiency of the inverse procedure

Multi-frequency identification of defects in conducting media

An eddy currents based procedure for the 3D image reconstruction of defects in metallic plates from multi-frequency data is presented. In particular, we exploit the collection of data at different probe positions as well as at different excitation frequencies in order to improve the amount of information content, the accuracy of the inverse methodology and its robustness against the experimental noise. The identification tool we developed, exploits the geometric A − χ formulation for the solution of the eddy-current forward problem together with a full nonlinear iterative inversion algorithm based on the total variation regularization.