Método multigrid algébrico: reutilização das estruturas multigrid no transporte de contaminantes

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

Finite-Elemente-Mehrgitter von Molekülen

Im Rahmen der Dichtefunktionaltheorie wurden Orbitalfunktionale wie z.B. B3LYP entwickelt. Diese lassen sich mit der „optimized effective potential“ – Methode selbstkonsistent auswerten. Während sie früher nur im 1D-Fall genau berechnet werden konnte, entwickelten Kümmel und Perdew eine Methode, bei der das OEP-Problem unter Verwendung einer Differentialgleichung selbstkonsistent gelöst werden kann. In dieser Arbeit wird ein Finite-Elemente-Mehrgitter-Verfahren verwendet, um die entstehenden Gleichungen zu lösen und damit Energien, Dichten und Ionisationsenergien für Atome und zweiatomige Moleküle zu berechnen. Als Orbitalfunktional wird dabei der „exakte Austausch“ verwendet; das Programm ist aber leicht auf jedes beliebige Funktional erweiterbar. Für das Be-Atom ließ sich mit 8.Ordnung –FEM die Gesamtenergien etwa um 2 Größenordnungen genauer berechnen als der Finite-Differenzen-Code von Makmal et al. Für die Eigenwerte und die Eigenschaften der Atome N und Ne wurde die Genauigkeit anderer numerischer Methoden erreicht. Die Rechenzeit wuchs erwartungsgemäß linear mit der Punktzahl. Trotz recht langsamer scf-Konvergenz wurden für das Molekül LiH Genauigkeiten wie bei FD und bei HF um 2-3 Größenordnungen bessere als mit Basismethoden erzielt. Damit zeigt sich, dass auf diese Weise benchmark-Rechnungen durchgeführt werden können. Diese dürften wegen der schnellen Konvergenz über der Punktzahl und dem geringen Zeitaufwand auch auf schwerere Systeme ausweitbar sein.

Um modelo de turbulência baseado no conceito de vórtice

O fenômeno da turbulência está presente na maioria dos escoamentos observados na indústria e na natureza. Muitas são as considerações a respeito das dificuldades relacionadas à caracterização dos escoamentos turbulentos. Uma das muitas questões trata do procedimento de análise do problema através da descrição estatística dos campos por grandezas “médias”, o que leva ao problema de fechamento e à modelagem do tensor de Reynolds, normalmente com modelos baseados no conceito de viscosidade turbulenta. Os modelos de turbulência já existentes apresentam algumas deficiências na previsão do escoamento, além de outras limitações, o que justifica a busca por novas abordagens para o tratamento da turbulência. Neste trabalho, o problema de fechamento é tratado segundo a modelagem turbulenta baseada no conceito de viscosidade turbulenta. Um novo modelo de turbulência é proposto, que admite a existência de vórtices imersos no escoamento e aplica conceitos e definições relacionados à identificação de vórtices, com o uso do critério de identificação Q , que caracteriza a região do escoamento ocupada pelo vórtice. Propõe-se a investigação da aplicabilidade do critério Q em conjunto com o modelo k − ε , para o desenvolvimento de um novo modelo de turbulência chamado k − ε −Q . Validou-se a aplicabilidade do modelo através de um código numérico computacional para tratamento de escoamentos turbulentos. A solução numérica foi obtida através da discretização do domínio fluido, utilizando o método de volumes finitos e o método multigrid foi utilizado para resolver o sistema linear resultante. Como verificação, foi utilizado este modelo de turbulência para simular o escoamento em uma cavidade quadrada com tampa deslizante e o escoamento turbulento sobre um degrau. Os resultados obtidos foram confrontados com dados experimentais e demonstraram que o modelo aqui proposto se apresenta mais eficiente que o clássico modelo k − ε , no tratamento da turbulência nesses dois problemas clássicos.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

A Multilevel Gradient Method for Optimization Problems

I problemi di ottimizzazione di dimensione finita di larga scala spesso derivano dalla discretizzazione di problemi di dimensione infinita. È perciò possibile descrivere il problema di ottimizzazione su più livelli discreti. Lavorando su un livello più basso di quello del problema considerato, si possono calcolare soluzioni approssimate che saranno poi punti di partenza per il problema di ottimizzazione al livello più fine. I metodi multilivello, già ampiamente presenti in letteratura a partire dagli anni Novanta, sfruttano tale caratteristica dei problemi di ottimizzazione per migliorare le prestazioni dei metodi di ottimizzazione standard. L’obiettivo di questa tesi è quello di implementare una variante multilivello del metodo del gradiente (MGM) e di testarlo su due diversi campi: la risoluzione delle Equazioni alle Derivate Parziali la ricostruzione di immagini. In questo elaborato viene illustrata la teoria dello schema multilivello e presentato l’algoritmo di MGM utilizzato nei nostri esperimenti. Sono poi discusse le modalità di utilizzo di MGM per i due problemi sopra presentati. Per il problema PDE, i risultati ottenuti mostrano un ottimo comportamento di MGM rispetto alla implementazione classica ad un livello. I risultati ottenuti per il problema di ricostruzione di immagini, al contrario delle PDEs, evidenziano come MGM sia efficace solo in determinate condizioni.

A Highly Improved Method For Sensitive Determination Of Amitriptyline In Pharmaceutical Formulations Using An Unmodified Carbon Nanotube Electrode In The Presence Of Sulfuric Acid.

The present paper describes a novel, simple and reliable differential pulse voltammetric method for determining amitriptyline (AMT) in pharmaceutical formulations. It has been described for many authors that this antidepressant is electrochemically inactive at carbon electrodes. However, the procedure proposed herein consisted in electrochemically oxidizing AMT at an unmodified carbon nanotube paste electrode in the presence of 0.1 mol L(-1) sulfuric acid used as electrolyte. At such concentration, the acid facilitated the AMT electroxidation through one-electron transfer at 1.33 V vs. Ag/AgCl, as observed by the augmentation of peak current. Concerning optimized conditions (modulation time 5 ms, scan rate 90 mV s(-1), and pulse amplitude 120 mV) a linear calibration curve was constructed in the range of 0.0-30.0 μmol L(-1), with a correlation coefficient of 0.9991 and a limit of detection of 1.61 μmol L(-1). The procedure was successfully validated for intra- and inter-day precision and accuracy. Moreover, its feasibility was assessed through analysis of commercial pharmaceutical formulations and it has been compared to the UV-vis spectrophotometric method used as standard analytical technique recommended by the Brazilian Pharmacopoeia.

Influence Of Delivery Method On Neuroprotection By Bone Marrow Mononuclear Cell Therapy Following Ventral Root Reimplantation With Fibrin Sealant.

The present work compared the local injection of mononuclear cells to the spinal cord lateral funiculus with the alternative approach of local delivery with fibrin sealant after ventral root avulsion (VRA) and reimplantation. For that, female adult Lewis rats were divided into the following groups: avulsion only, reimplantation with fibrin sealant; root repair with fibrin sealant associated with mononuclear cells; and repair with fibrin sealant and injected mononuclear cells. Cell therapy resulted in greater survival of spinal motoneurons up to four weeks post-surgery, especially when mononuclear cells were added to the fibrin glue. Injection of mononuclear cells to the lateral funiculus yield similar results to the reimplantation alone. Additionally, mononuclear cells added to the fibrin glue increased neurotrophic factor gene transcript levels in the spinal cord ventral horn. Regarding the motor recovery, evaluated by the functional peroneal index, as well as the paw print pressure, cell treated rats performed equally well as compared to reimplanted only animals, and significantly better than the avulsion only subjects. The results herein demonstrate that mononuclear cells therapy is neuroprotective by increasing levels of brain derived neurotrophic factor (BDNF) and glial derived neurotrophic factor (GDNF). Moreover, the use of fibrin sealant mononuclear cells delivery approach gave the best and more long lasting results.

Uv-vis Spectra As An Alternative To The Lowry Method For Quantify Hair Damage Induced By Surfactants.

It is well known that long term use of shampoo causes damage to human hair. Although the Lowry method has been widely used to quantify hair damage, it is unsuitable to determine this in the presence of some surfactants and there is no other method proposed in literature. In this work, a different method is used to investigate and compare the hair damage induced by four types of surfactants (including three commercial-grade surfactants) and water. Hair samples were immersed in aqueous solution of surfactants under conditions that resemble a shower (38 °C, constant shaking). These solutions become colored with time of contact with hair and its UV-vis spectra were recorded. For comparison, the amount of extracted proteins from hair by sodium dodecyl sulfate (SDS) and by water were estimated by the Lowry method. Additionally, non-pigmented vs. pigmented hair and also sepia melanin were used to understand the washing solution color and their spectra. The results presented herein show that hair degradation is mostly caused by the extraction of proteins, cuticle fragments and melanin granules from hair fiber. It was found that the intensity of solution color varies with the charge density of the surfactants. Furthermore, the intensity of solution color can be correlated to the amount of proteins quantified by the Lowry method as well as to the degree of hair damage. UV-vis spectrum of hair washing solutions is a simple and straightforward method to quantify and compare hair damages induced by different commercial surfactants.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.

Trichomes Related To An Unusual Method Of Water Retention And Protection Of The Stem Apex In An Arid Zone Perennial Species.

It is well known that trichomes protect plant organs, and several studies have investigated their role in the adaptation of plants to harsh environments. Recent studies have shown that the production of hydrophilic substances by glandular trichomes and the deposition of this secretion on young organs may facilitate water retention, thus preventing desiccation and favouring organ growth until the plant develops other protective mechanisms. Lychnophora diamantinana is a species endemic to the Brazilian 'campos rupestres' (rocky fields), a region characterized by intense solar radiation and water deficits. This study sought to investigate trichomes and the origin of the substances observed on the stem apices of L. diamantinana. Samples of stem apices, young and expanded leaves were studied using standard techniques, including light microscopy and scanning and transmission electron microscopy. Histochemical tests were used to identify the major groups of metabolites present in the trichomes and the hyaline material deposited on the apices. Non-glandular trichomes and glandular trichomes were observed. The material deposited on the stem apices was hyaline, highly hydrophilic and viscous. This hyaline material primarily consists of carbohydrates that result from the partial degradation of the cell wall of uniseriate trichomes. This degradation occurs at the same time that glandular trichomes secrete terpenoids, phenolic compounds and proteins. These results suggest that the non-glandular trichomes on the leaves of L. diamantinana help protect the young organ, particularly against desiccation, by deposition of highly hydrated substances on the apices. Furthermore, the secretion of glandular trichomes probably repels herbivore and pathogen attacks.

Tissue Microarray Is A Reliable Method For Immunohistochemical Analysis Of Pleomorphic Adenoma.

To determine the most adequate number and size of tissue microarray (TMA) cores for pleomorphic adenoma immunohistochemical studies. Eighty-two pleomorphic adenoma cases were distributed in 3 TMA blocks assembled in triplicate containing 1.0-, 2.0-, and 3.0-mm cores. Immunohistochemical analysis against cytokeratin 7, Ki67, p63, and CD34 were performed and subsequently evaluated with PixelCount, nuclear, and microvessel software applications. The 1.0-mm TMA presented lower results than 2.0- and 3.0-mm TMAs versus conventional whole section slides. Possibly because of an increased amount of stromal tissue, 3.0-mm cores presented a higher microvessel density. Comparing the results obtained with one, two, and three 2.0-mm cores, there was no difference between triplicate or duplicate TMAs and a single-core TMA. Considering the possible loss of cylinders during immunohistochemical reactions, 2.0-mm TMAs in duplicate are a more reliable approach for pleomorphic adenoma immunohistochemical study.

Use Of Experimental Design To Optimize A Triple-potential Waveform To Develop A Method For The Determination Of Streptomycin And Dihydrostreptomycin In Pharmaceutical Veterinary Dosage Forms By Hplc-pad.

An HPLC-PAD method using a gold working electrode and a triple-potential waveform was developed for the simultaneous determination of streptomycin and dihydrostreptomycin in veterinary drugs. Glucose was used as the internal standard, and the triple-potential waveform was optimized using a factorial and a central composite design. The optimum potentials were as follows: amperometric detection, E1=-0.15V; cleaning potential, E2=+0.85V; and reactivation of the electrode surface, E3=-0.65V. For the separation of the aminoglycosides and the internal standard of glucose, a CarboPac™ PA1 anion exchange column was used together with a mobile phase consisting of a 0.070 mol L(-1) sodium hydroxide solution in the isocratic elution mode with a flow rate of 0.8 mL min(-1). The method was validated and applied to the determination of streptomycin and dihydrostreptomycin in veterinary formulations (injection, suspension and ointment) without any previous sample pretreatment, except for the ointments, for which a liquid-liquid extraction was required before HPLC-PAD analysis. The method showed adequate selectivity, with an accuracy of 98-107% and a precision of less than 3.9%.

A Rapid And Simple Capillary Electrophoresis Method For Indirect Determination Of The Biocide 2,2-dibromo-3-nitrilo-propionamide (dbnpa) In Cooling Waters.

A capillary zone electrophoresis (CE) method was developed for the determination of the biocide 2,2-dibromo-3-nitrilo-propionamide (DBNPA) in water used in cooling systems. The biocide is indirectly determined by CE measurement of the concentration of bromide ions produced by the reaction between the DBNPA and bisulfite. The relationship between the bromide peak areas and the DBNPA concentrations showed a good linearity and a coefficient of determination (R(2)) of 0.9997 in the evaluated concentration range of 0-75 μmol L(-1). The detection and quantification limits for DBNPA were 0.23 and 0.75 μmol L(-1), respectively. The proposed CE method was successfully applied for the analysis of samples of tap water and cooling water spiked with DBNPA. The intra-day and inter-day (intermediary) precisions were lower than 2.8 and 6.2%, respectively. The DBNPA concentrations measured by the CE method were compared to the values obtained by a spectrophotometric method and were found to agree well.