1,721,109 research outputs found
Fast Frequency and Material Properties Sweeps for Quasi-Static Problems
No full textWe introduce a novel technique that speeds up the computation of a frequency sweep or some parametric change of material properties - assumed uniform over the entire domain - around a nominal value in electroquasi-static problem or magnetoquasi-static problem. In place of using the usual practice of solving the complex systems arising at each frequency and at each material parameter value independently, our technique requires only one factorization of a real, symmetric, and positive definite matrix. The solution at each frequency and each value of material parameter is, then, found with a few back-substitutions only. The obtained speedup is sensible and the implementation is straightforward, showing the usefulness of the proposed technique in practical applications. © 1965-2012 IEEE
Optimal cohomology generators for 2d eddy-current problems in linear time
No full textThe aim of this paper is to present an automatic and efficient algorithm to find cohomology generators suitable for 2d eddycurrent problems formulated by means of complementary formulations. The algorithm is general, straightforward to implement, exhibits a linear worst-case computational complexity and produces optimal representatives of generators. By optimal we mean the representatives that minimize in practical cases the fill-in of the system of equations matrix and guarantee that the current flowing in each conductor is in one-to-one correspondence with a generator. As a numerical example, the complementary formulations are used to compute the frequency-dependent per-unit-length impedance in integrated circuits
Lean Complementarity for Poisson Problems
No full textWe introduce a novel technique - lean complementarity - that attempts to eliminate any waste of computational resources occurring during the pursuing of complementarity. First, contrarily to the widely used practice of solving the problem two times with a pair of complementary or complementary-dual formulations, lean complementarity requires just one solution with the computationally cheap formulation based on the scalar potential. This result is enabled by a novel and explicit flux equilibration technique that produces tight bounds and is computationally inexpensive, because no system has to be solved. Second, the systems arising during the adaptive mesh refinement procedure are solved inexactly on purpose, by stopping the iterations of the iterative solver when the algebraic error gets negligible with respect to the discretization error. The discretization error is bounded with complementarity, whereas the algebraic error is computed very accurately with a novel and cheap technique. © 1965-2012 IEEE
Numerical determination of upper and lower bounds of the transmembrane potential with complementarity
No full textOne stroke complementarity for poisson-like problems
No full textTaking electrokinetics as a paradigm problem for the sake of simplicity, complementarity originates when an irrotational electric field and a solenoidal current density satisfying boundary conditions are in hand. We first compare three formulations to obtain a solenoidal current density, both in terms of pure computational advantage and in the ability to pursue symmetric energy bounds with respect to the standard electric scalar potential formulation. For these formulations, we devise post-processing techniques that promise to provide bilateral bounds in one stroke, hence requiring the solution of just one linear system
Diagonal discrete hodge operators for simplicial meshes using the signed dual complex
No full textWe present a technique to extend the geometric construction of diagonal discrete Hodge operators to arbitrary triangular and tetrahedral boundary conforming Delaunay meshes in the frequent case of piecewise uniform and isotropic material parameters. The technique is based on the novel concept of signed dual complex that originates from a physical argument. In particular, it is shown how the positive definiteness of the mass matrix obtained with the signed dual complex is easily ensured for all boundary conforming Delaunay meshes without requiring—as expected by the common knowledge—that each circumcenter has to lie inside the corresponding element. Eliminating this requirement, whose fulfillment presents otherwise formidable practical difficulties, enables
one to easily obtain efficient, consistent, and stable schemes
Extraction of VLSI multiconductor transmission line parameters by complementarity
No full textSolving 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
Complementary geometric formulations for electrostatics
No full textThe simultaneous use of a pair of complementary discrete formulations for electrostatic boundary value problems (BVPs) allows to accurately compute electromagnetic quantities, such as capacitance or electrostatic force with a minimum computational effort. In fact, the two formulations provide the upper and lower bounds for these quantities and their averages result quite close to the exact solution even for extremely coarse meshes. Despite the potential benefit to the many three-dimensional large-scale applications, taking advantage of this feature is not exploited in practice due to theoretical difficulties in the potential design. The aim of this paper is to fill this gap by rigorously introducing a pair of three-dimensional complementary geometric formulations to solve electrostatic BVPs on domains covered by conformal polyhedral meshes. In particular, an original formulation based on a vector potential is introduced by using cohomology theory with integer coefficients. It is shown how the so-called thick links are needed, which are representatives of the second cohomology group generators of the dielectric region. Two easy-to-implement graph-theoretic algorithms to automatically find such a basis with optimal computational complexity are described. Some benchmark problems are presented to show how the simultaneous use of both formulations yields to a sensible computational advantage. Therefore, solvers based on complementary formulations should be embedded in the next-generation of electromagnetic Computer-Aided Engineering (CAE) softwares
Advanced Geometric Formulations for the Design of a Long Defects Detection System
No full textThe aim of the paper is to highlight some of the innovative methodologies, techniques and systems for nondestructive electromagnetic testing, which have been developed in the framework of the applications of methods of a diagnostics electromagnetic project partially funded by the Italian Ministry of University and Research. In particular, we will present the feasibility design of a suitable exciting-receiving coils configuration able to detect long defects by means of eddy-currents. To solve the forward eddy-currents problem, advanced analysis tools have been developed and validated
Geometry of the 3D Schroedinger problem and comparison with Finite Elements discretization
No full textThe numerical modeling of nanoscale electron devices needs the development of accurate and efficient numerical methods, in
particular, for the numerical solution of the Schrödinger problem. If FEMs allow an accurate geometric representation of the device,
they lead to a discrete counterpart of Schrödinger problem in terms of a computationally heavy generalized eigenvalue problem.
Exploiting the geometric structure behind the Schrödinger problem, we will construct a numerically efficient discrete counterpart
of it, yielding to a standard eigenvalue problem. We will also show how the two approaches are only partially akin to each other
even when lumping is applied
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