Monotone methods on non-matching grids for non-linear contact problems

Nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We use a generalized mortar method based on dual Lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies. In the case of unilateral contact problems, pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers. Here, we generalize these techniques to nonmatching triangulations, where the constraints are realized in terms of weak integral conditions. The basic new idea is the construction of a nested sequence of nonconforming constrained spaces. We use suitable basis transformations and a multiplicative correction. In contrast to other approaches, no outer iteration scheme is required. The resulting monotone method is of optimal complexity and can be implemented as a multigrid method. Numerical results illustrate the performance of our approach in two and three dimensions

Nonconforming decomposition methods: Techniques for linear elasticity

Mortar finite element methods provide a powerful tool for the numerical approximation of partial differential equations. Many domain decomposition techniques based on the coupling of different discretization schemes or of nonmatching triangulations along interior interfaces can be analyzed within this framework. Here, we present a mortar formulation based on dual basis functions and a special multigrid method. The starting point for our multigrid method is a symmetric positive definite system on the unconstrained product space. In addition, we introduce a new algorithm for the numerical solution of a nonlinear contact problem between two linear elastic bodies It will be shown that our method can be interpreted as an inexact Dirichlet-Neumann algorithm for the nonlinear problem. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from a mortar discretization on non-matching triangulations with dual basis Lagrange multipliers. Numerical results illustrate the performance of our approach in 2D and 3D

Domain decomposition methods on nonmatching grids and some applications to linear elasticity problems

Domain decomposition techniques provide a powerful tool for the coupling of different discretization methods or nonmatching triangulations across subregion boundaries. Here, we consider mortar finite elements methods for linear elasticity and diffusion problems. These domain decomposition techniques provide a more flesible approach than standard conforming formulations. The mortar solution is weakly continuous at subregion boundaries, and its jump is orthogonal to a suitable Lagrange multiplier space. Our approach is based on dual bases for the Lagrange true for the standard mortar method [2]. The biorthogonality relation guarantees that the Lagrange multiplier can be locally eliminated, and that we obtain a symmetric positive semidefinite system on the unconstrained product space. This system will be solved by multigrid techniques. Numerical results illustrate the performance of the multigrid method in 2D and 3D

Produtos químicos perigosos utilizados em laboratórios de ensino: proposta e exemplos para indicação de seus perigos no rótulo

Typically hundreds of different chemical products stored in small flasks which cannot accommodate labels large enough to bear all information required by the Globally Harmonised System of Classification, Labelling and Packaging of Chemicals (GHS) are used in academic laboratories. To overcome this restriction Brazilian legislation permits communication of the dangers of chemical products to trained laboratory workers/students by alternative means. Here we describe an alternative label system, developed by the German Social Accident Insurance (DGUV), which allows hazard communication to trained workers/students via a labelling system, using pictograms and highly condensed hazard statements to alert about dangerous chemical products

The association between body-mass index and patient outcome in septic shock: a retrospective cohort study

Zusammenfassung: HINTERGRUND: Es bestehen keine Daten über die Assoziation zwischen dem Body Mass Index (BMI) bzw. BMI Kategorien und der Mortalität von septischen Schock-patienten. METHODEN: Die Datenbank einer interdisziplinären Intensivstation wurde retrospektiv nach erwachsenen Patienten mit septischem Schock durchsucht. Von allen Patienten wurde der BMI, demographische, klinische und laborchemische Parameter gemeinsam mit Outcomevariabeln dokumentiert. Die Studienpatienten wurden wie folgt anhand des BMI kategorisiert: BMI 30 kg/m2, Fettleibigkeit. Bivariate und multivariate logistische Regressionsmodelle wurden verwendet, um den Zusammenhang zwischen dem BMI und Outcome-variabeln zu untersuchen. RESULTATE: 301 septische Schockpatienten wurden identifiziert. Der BMI war bivariat mit der Mortalität auf der Intensivstation assoziiert (OR, 0,91; 95% CI, 0,86-0,98; p = 0,007). Es gab keine signifikante Assoziation zwischen dem BMI und der Mortalität auf der Intensivstation. Allerdings waren höhere BMI Werte trendmässig mit einer niedrigeren Intensivstations-mortalität assoziiert (OR, 0,93; 95% CI, 0,86-1,01; p = 0,09). Während übergewichtige (OR, 0,43; 95% CI, 0,19-0,98; p = 0,04) und fettleibige (OR, 0,28; 95% CI, 0,08-0,93; p = 0,04) Patienten ein unabhängig niedrigeres Risiko auf der Intensivstation zu versterben hatten als normalgewichtige Patienten, gab es keinen Unterschied im Sterberisiko zwischen normal- und untergewichtigen Patienten (p = 0,22). Ein hoher BMI war unabhängig mit einer geringen Häufigkeit eines akutem Deliriums (p = 0,04) und einer geringeren Intensivwieder-aufnahmerate (p = 0,001), aber mit mehr Harnwegsinfektionen (p = 0,02) assoziiert. SCHLUSSFOLGERUNG: Bis zu einem BMI von 50 kg/m2 scheint keine Assoziation zwischen BMI und schlechterem Überleben auf der Intensivstation oder im Krankenhaus bei septischen Schockpatienten zu bestehen. Im Gegenteil, hohe BMI Werte könnten sogar das Risiko am septischen Schock zu versterben reduziere

Antibiotics mineralization by electrochemical and UV-based hybrid processes: evaluation of the synergistic effect

[EN] Antibiotics are not efficiently removed in conventional wastewater treatments. In fact, different advanced oxidation process (AOPs), including ozone, peroxide, UV radiation, among others, are being investigated in the elimination of microcontaminants. Most of AOPs proved to be efficient on the degradation of antibiotics, but the mineralization is on the one hand not evaluated or on the other hand not high. At this work, the UV-based hybrid process, namely Photo-assisted electrochemical oxidation (PEO), was applied, aiming the mineralization of microcontaminants such as the antibiotics Amoxicillin (AMX), Norfloxacin (NOR) and Azithromycin (AZI). The influence of the individual contributions of electrochemical oxidation (EO) and the UV-base processes on the hybrid process (PEO) was analysed. Results showed that AMX and NOR presented higher mineralization rate under direct photolysis than AZI due to the high absorption of UV radiation. For the EO processes, a low mineralization was found for all antibiotics, what was associated to a mass-transport limitation related to the low concentration of contaminants (200 ¿g/L). Besides that, an increase in mineralization was found, when heterogeneous photocatalysis and EO are compared, due to the influence of UV radiation, which overcomes the mass-transport limitations. Although the UV-based processes control the reaction pathway that leads to mineralization, the best results to mineralize the antibiotics were achieved by PEO hybrid process. This can be explained by the synergistic effect of the processes that constitute them. A higher mineralization was achieved, which is an important and useful finding to avoid the discharge of microcontaminants in the environment.The authors thank CAPES project number DGPU-2015/7595/14-0, CNPq, FAPERGS, Cyted and FINEP for the financial support.Da Silva, SW.; Heberle, AN.; Santos, AP.; Rodrigues, M.; Valentín Pérez-Herranz; Bernardes, A. 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A monotone multigrid solver for two body contact problems in biomechanics

The purpose of the paper is to apply monotone multigrid methods to static and dynamic biomechanical contact problems. In space, a finite element method involving a mortar discretization of the contact conditions is used. In time, a new contact-stabilized Newmark scheme is presented. Numerical experiments for a two body Hertzian contact problem and a biomechanical application are reported

The association between body-mass index and patient outcome in septic shock: a retrospective cohort study

It is unknown whether body-mass index (BMI) and commonly defined BMI categories are associated with mortality in patients with septic shock