Domain decomposition preconditioners of Neumann-Neumann type for hp‐approximations on boundary layer meshes in three dimensions

We develop and analyse Neumann-Neumann methods for hp finite‐element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. These are meshes that are highly anisotropic where the aspect ratio typically grows exponentially with the polynomial degree. The condition number of our preconditioners is shown to be independent of the aspect ratio of the mesh and of potentially large jumps of the coefficients. In addition, it only grows polylogarithmically with the polynomial degree, as in the case of p approximations on shape‐regular meshes. This work generalizes our previous one on two‐dimensional problems in Toselli & Vasseur (2003a, submitted to Numerische Mathematik, 2003c to appear in Comput. Methods Appl. Mech. Engng.) and the estimates derived here can be employed to prove condition number bounds for certain types of FETI method

Dual-primal FETI algorithms for edge finite-element approximations in 3D

A family of dual-primal finite-element tearing and interconnecting methods for edge-element approximations in 3D is proposed and analysed. The key part of this work relies on the observation that for these finite-element spaces there is a strong coupling between degrees of freedom associated with subdomain edges and faces and a local change of basis is therefore necessary. The primal constraints are associated with subdomain edges. We propose three methods. They ensure a condition number that is independent of the number of substructures and possibly large jumps of one of the coefficients of the original problem, and only depends on the number of unknowns associated with a single substructure, as for the corresponding methods for continuous nodal elements. A polylogarithmic dependence is shown for two algorithms. Numerical results validating our theoretical bounds are give

Free space optical system performance for a Gaussian beam propagating through non Kolmogorov weak turbulence

Atmospheric turbulence has been described for many years by Kolmogorov's power spectral density model because of its simplicity. Unfortunately several experiments have been reported recently that show Kolmogorov theory is sometimes incomplete to describe atmospheric statistics properly, in particular in portions of the troposphere and stratosphere. It is known that free space laser system performance is limited by atmospheric turbulence. In this paper we use a non-Kolmogorov power spectrum which uses a generalized exponent instead of constant standard exponent value 11/3 and a generalized amplitude factor instead of constant value 0.033. Using this spectrum in weak turbulence, we carry out, for a Gaussian beam propagating along a horizontal path, analysis of long term beam spread, scintillation, probability of fade, mean signal to noise ratio and mean bit error rate as variation of the spectrum exponent. Our theoretical results show that for alpha values lower than 11/3 , but not for alpha close to 3 , there is a remarkable increase of scintillation and consequently a major penalty on the system performance. However when alpha assumes values close to 3 or for alpha values higher than 11/3 scintillation decreases leading to an improvement on the system performanc

A novel verification system for handwritten words recognition

International audienceIn the field of isolated handwritten word recognition, the development of highly effective verification systems to reject words presenting ambiguities is still an active research topic. In this paper, a novel verification system based on support vector machine scoring and multiple reject class-dependent thresholds is presented. In essence, a set of support vector machines appended to a standard HMM-based recognition system provides class-dependent confidence measures employed by the verification mechanism to accept or reject the recognized hypotheses. Experimental results on RIMES database show that this approach outperforms other state-of-the-art approaches

Handwritten word verification by SVM-based hypotheses re-scoring and multiple thresholds rejection

International audienceIn the field of isolated handwritten word recognition, the development of verification systems that optimize the trade-off between performance and reliability is still an active research topic. To minimize the recognition errors, usually, a verification system is used to accept or reject the hypotheses produced by an existing recognition system. In this paper, a novel verification architecture is presented. In essence, the recognition hypotheses, re-scored by a set of the support vector machines, are validated by a verification mechanism based on multiple rejection thresholds. In order to tune these (class-dependent) rejection thresholds, an algorithm based on dynamic programming is proposed which focus on maximizing the recognition rate for a given prefixed error rate

Mixed HP -finite element approximations on geometric edge and boundary layer meshes in three dimensions

Summary: In this paper, we consider the Stokes problem in a three-dimensional polyhedral domain discretized with hp finite elements of type Qk for the velocity and Qk-2 for the pressure, defined on hexahedral meshes anisotropically and non quasi-uniformly refined towards faces, edges, and corners. The inf-sup constant of the discretized problem is independent of arbitrarily large aspect ratios. Our work generalizes a recent result for two-dimensional problems in [10, 11

Prevalence and Tracking of Weight Disorders in Italian Primary School Students: A Three-Year Follow-Up

Obesity has been widely described as the latest epidemic, and in some areas obesity co-exists with undernutrition. The purpose of this study was to assess the variability of weight status of a cohort of 279 Italian primary school students followed longitudinally for three years. Overweight was the most common weight status disorder in both sexes and generally prevailed in females. Underweight was also more frequent in females than males, while males generally showed a higher incidence of obesity. Overweight showed the highest stability in females. In males, tracking of overweight was 62.5%, while that of normal weight was 89.36%. Overweight tracks through the three consecutive years in a high percentage of both sexes. In the whole sample (regardless of sex and weight category), overweight shows the highest increase over the three-year period. This study provides public health professionals with useful data for policy planning in regard to childhood obesity