<p>In this work, we proposed a spectral integral method (SIM)-spectral element method (SEM)- finite element method (FEM) domain decomposition method (DDM) for solving inhomogeneous multi-scale problems. The proposed SIM-SEM-FEM domain decomposition algorithm can efficiently handle problems with multi-scale structures, </p><p>by using FEM to model electrically small sub-domains and using SEM to model electrically large and smooth sub-domains. The SIM is utilized as an efficient boundary condition. This combination can reduce the total number of elements used in solving multi-scale problems, thus it is more efficient than conventional FEM or conventional FEM domain decomposition method. Another merit of the proposed method is that it is capable of handling arbitrary non-conforming elements. Both geometry modeling and mesh generation are totally independent for different sub-domains, thus the geometry modeling and mesh generation are highly flexible for the proposed SEM-FEM domain decomposition method. As a result, the proposed SIM-SEM-FEM DDM algorithm is very suitable for solving inhomogeneous multi-scale problems.</p> / Dissertation

The study of catalytic oxidation on the removal of NO was investigated over the Cu-catalysts . The Cu-catalysts , including Cu/TiO2 , Cu/Al2O3 and Cu/SiO2 , were prepared by impregnation method . Alougth NO2 , the product of this reaction , has higher toxicity than NO , but it might be removed completely by absorption with H2O or alkalinal solution for its high solubility . The experiments can be divided into three parts , i.e. , the screen of test catalysts , the effect of operating factors on the conversion of NO and the kinetic model . In the first part , the activity of test catalysts , which were prepared by mixing three various sources of Cu-ions¡]i.e., Cu(NO3)2 , Cu(CH3COO)2 , and CuSO4¡^with three different types of support¡]i.e., TiO2 , Al2O3 , and SiO2¡^, and were compared in form of conversion on NO to find the best catalyst . The results show that the mixture Cu(NO3)2 / TiO2 has the good performance on the conversion of NO , and also has more wider operating in range of temperature . In order to find the optimal loading of Cu on Cu(NO3)2 / TiO2 , additional test of various dosage over the catalysts was conduct in series . It is found that 8wt.% of Cu loading on Cu(NO3)2 / TiO2 is the most economic dosage . Therefore , we select this type of Cu oxide as the best catalyst in the following work . In the second part , the effect of NO inlet concentration , space velocity and humidity on the conversion of NO were performed . The results show that the conversion of NO decreases with the increasing of [NO]in when [NO]in is larger than 1000ppm¡Fthe conversion of NO is not changed with [NO]in when [NO]in is lower than 1000ppm . The better space velocity is 15000hr-1 , i.e.,the empty bed residence time is 0.24 second . The reaction on NO conversion would be restrained by higher humidity contenting in inlet gas stream , but the effect of inhibition on NO conversion is not significant . Finally , the kinetics of the oxidation of NO over 8wt.% Cu(NO3)2 / TiO2 was obtained by integral method .It is found that the oxidations of NO can be described by first order reversible reaction and the observed activation energy are 15.8 kcal/mole¡]forward reaction¡^and 25.9 kcal/mole¡]backward reaction¡^, respectively . By comparing the conversion of predicted NO with the experimentals , we can find the suitable operation conditions in application of the kinetic model : the inlet concentration of NO in a range of 300-1000ppm , the empty-bed residence time ranging from 0.12-0.48 second , and the absolute humidity ranging from 4854 to 42475ppm .

Remiantis silpnąja Galiorkino formuluote darbe sukonstruoti trys paprastųjų diferencialinių lygčių integravimo metodai. Tyrinėtas metodų konvergavimas remiantis skaitiniais integravimo rezultatais, bei metodų tikslumas lyginant rezultatus su tiksliuoju sprendinių ir kitų integratorių rezultatais. / Three integrators of ordinary diferential equations based on Galiorkin's weak formulation were constructed in this work. The precision of ontegrators is evaluated numerically,by comparing the result with exact first integral and the solution got using Runge-Kutto method.

Modeling of wave scattering from grating couplers has become increasingly important due to extensive recent research interest in the problem of plasmonic resonance. Computational algorithms which are specially used to model the problem of scattering from the grating surfaces suffer from several drawbacks such as accuracy, computational efficiency, and generality. To address the challenges of the previous methods, this work presents a novel hybrid Finite Element-Boundary Integral Method (FE-BIM) solution to the problem of scattering from grating surfaces consisting of finite or infinite array of two-dimensional cavities and holes in an infinite metallic walls covered with a stratified dielectric layer. To solve the scattering problem from finite number of cavities or holes engraved in a perfectly conducting screen (PEC), the solution region is divided into interior regions containing the cavities or holes and the region exterior to them. The finite element formulation is applied inside the interior region to derive a linear system of equations associated with nodal field values. Using two-boundary formulation, the surface integral equation employing free-space Green's function is then applied at \emph{only} the opening of the cavities or holes to truncate the computational domain and to connect the matrix subsystem generated from each cavity or hole. The hybrid FE-BIM method is extended to solve the scattering problem from an infinite array of cavities or holes in a PEC screen by deriving the quasi-periodic Green's function. In the scattering problem from an infinite array of cavities, the finite element formulation is first used inside a single cavity in the unit-cell. Next, the surface integral equation employing the quasi-periodic Green's function is applied at the opening of \emph{only} a single cavity as a boundary constraint to truncate the computational domain. Effect of the infinite array of cavities is incorporated into the system of the nodal equations by the quasi-periodic Green's function. Finally, the method based on the hybrid FE-BIM is developed to solve the scattering problem from grating surfaces covered with a stratified dielectric layer. In this method, the surface integral equation employing grounded dielectric slab Green's function is applied at the opening of the cavities or holes inside the dielectric coating to truncate the solution region efficiently. An accurate algorithm is presented to derive the grounded dielectric slab Green's function in spatial domain incorporating the effects of the surface-waves and leaky-waves excited and propagated inside the dielectric slab. Numerical examples of near and far field calculations for finite or infinite array of cavities or holes are presented to validate accuracy, versatility, and efficiency of the algorithm presented in this thesis.

Computational fluid dynamics (CFD) simulation is a computational tool for exploring flow applications in science and technology. Of central importance in many flow scenarios is the accurate modelling of the boundary layer phenomenon. This is particularly true in the aerospace industry, where it is central to the prediction of drag. Modern CFD codes as applied to modelling aerodynamic flows have to be fast and efficient in order to model complex realistic geometries. When considering viscous flows, the boundary layer typically requires the largest part of computational resources. To simulate boundary layer flow with most current CFD codes, requires extremely fine mesh spacing normal to the wall and is consequently computationally very expensive. Boundary layer modelling approaches offer considerable computational cost savings. One boundary layer method which proved to be very accurate is the two-integral method of Drela (1985). Coupling the boundary layer solution to inviscid external flow, however, is a challenge due to the Goldstein singularity, which occurs as separation is approached. This research proposed to develop a new method to couple Drela‟s two-integral equations to a generic outer flow solver in an iterative fashion. The study introduced an auxiliary equation, which was solved along with the displacement thickness to overcome the Goldstein singularity without the need to solve the entire flow domain simultaneously. In this work, the incompressible Navier-Stokes equations were used for the outer flow. In the majority of previous studies, the boundary layer thickness was simulated using a wall transpiration boundary condition at the interface between viscous and inviscid flows. This boundary condition was inherently non-physical since it added extra mass into the system to simulate the effects of the boundary layer. Here, this drawback was circumvented by the use of a mesh movement algorithm to shift the surface of the body outward without regridding the entire mesh. This replaced the transpiration boundary condition. The results obtained show that accurate modelling is possible for laminar incompressible flow. The predicted solutions obtained compare well with similarity solutions in the case of flat and inclined plates, and with the results of a NACA0012 airfoil produced by the validated XFOIL code (Drela and Youngren, 2001). Copyright / Dissertation (MEng)--University of Pretoria, 2012. / Mechanical and Aeronautical Engineering / unrestricted

This study aims to develop a computer program to perform finite elements based fracture mechanics analyses of three dimensional surface cracks in T-welded joints of construction machinery. The geometrical complexity of the finite elements models and the requirement of large computer resources for the analyses necessitate the use of shell elements for general stress distribution optimization. A sub-modeling technique, together with a shell to solid conversion method, enables the user to model a local region and analyze it by defining the weld and crack parameters. It is assumed that the weld material is the same with the sheet metal material and the surface cracks are considered to occur on two weld toes and weld root. The surface cracks are assumed to have a semi elliptical crack front profile. In order to simulate the square-root strain singularity around the crack front, collapsed 20-node three dimensional brick elements are utilized. The rest of the local model is modeled by using 20-node three dimensional brick elements. The main objective of this work is to calculate the mixed mode energy release rates around the crack front for a sub-model of a global shell model by using J-integral method.

Efficient electromagnetic solvers based on surface integral equations (SIEs) are developed for the analysis of scattering from large-scale and complex composite structures that consist of piecewise homogeneous magnetodielectric and perfect electrically/magnetically conducting (PEC/PMC) regions. First, a multiple-grid extension of the adaptive integral method (AIM) is presented for multi-region problems. The proposed method accelerates the iterative method-of-moments solution of the pertinent SIEs by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of K homogeneous regions, it introduces K different auxiliary grids. It uses the k^{th} auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection/anterpolation, propagation, interpolation, and near-zone pre-correction stages in the k^{th} region. Thus, the AIM stages are executed a total of K times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O(N^{nz,near}+sum({N_k}^Clog{N_k}^C)) operations per iteration, where N^{nz,near} denotes the total number of near-zone interactions in all regions and {N_k}^C denotes the number of nodes of the k^{th} Cartesian grid. Numerical results validate the method’s accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to 10^6 degrees of freedom and 10^3 regions). Then, a Green function modification approach and a scheme of Hankel- to Teoplitz-matrix conversions are efficiently incorporated to the multiple-grid AIM method to account for a PEC/PMC plane. Theoretical analysis and numerical examples show that, compared to a brute-force imaging scheme, the Green function modification approach reduces the simulation time and memory requirement by a factor of (almost) two or larger if the structure of interest is terminated on or resides above the plane, respectively. In addition, the SIEs are extended to cover structures composed of metamaterial regions, PEC regions, and PEC-material junctions. Moreover, recently introduced well-conditioned SIEs are adopted to achieve faster iterative solver convergence. Comprehensive numerical tests are performed to evaluate the accuracy, computational complexity, and convergence of the novel formulation which is shown to significantly reduce the number of iterations and the overall computational work. Lastly, the efficiency and capabilities of the proposed solvers are demonstrated by solving complex scattering problems, specifically those pertinent to analysis of wave propagation in natural forested environments, the design of metamaterials, and the application of metamaterials to radar cross section reduction. / text

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-26T17:27:53Z No. of bitstreams: 1 monicacristinamelquiadesduque.pdf: 697556 bytes, checksum: bf32f50f1172cd3d5154fa9a1bbb5219 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-13T12:03:30Z (GMT) No. of bitstreams: 1 monicacristinamelquiadesduque.pdf: 697556 bytes, checksum: bf32f50f1172cd3d5154fa9a1bbb5219 (MD5) / Made available in DSpace on 2017-05-13T12:03:30Z (GMT). No. of bitstreams: 1 monicacristinamelquiadesduque.pdf: 697556 bytes, checksum: bf32f50f1172cd3d5154fa9a1bbb5219 (MD5) Previous issue date: 2013-02-20 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresenta-se aqui uma discussão sobre três métodos para o cálculo do propagador de Feynman para alguns modelos em mecânica quântica não relativística. O formalismo de Feynman é apenas um dos vários existentes para a abordagem de problemas na mecânica quântica. O primeiro método é um cálculo da integral de caminho, que é baseado em uma relação de recorrência para a produção de propagadores infinitesimais. Essa relação de recorrência não tem aparecido em discussões anteriores da integral de caminho do oscilador harmônico unidimensional, embora seja inspirada por uma relação similar em um sistema tridimensional. O segundo método foi desenvolvido por Schwinger em 1951 para tratar ações efetivas na eletrodinâmica quântica baseado na solução das equações de movimento do operador de Heisenberg. Com o uso adequado do operador ordenado e subordinadas as condições iniciais produz o propagador. Por fim, o terceiro método, que usa-se de técnicas algébricas baseadas na fatoração do operador evolução temporal usando a fórmula Baker-Campbell-Hausdorff. / Here we present a discussion of three methods to calculate the Feynman propagator for some models in non-relativistic quantum mechanics. The formalism of Feynman is just one of several available for addressing problems in quantum mechanics. The first method is a calculation of the integral path, which is based on a recurrence relation for the production of infinitesimal propagators. This recurrence relation has not appeared in previous discussions of the full path of the one-dimensional harmonic oscillator, although inspired by a similar relationship in a three-dimensional system. The second method was developed by Schwinger in 1951 for treating effective action in quantum electrodynamics based on the solution of the equations of motion of the Heisenberg operator. With the proper use of the operator ordained and subordinated the initial conditions produces the propagator. Finally, the third method, which uses the algebraic techniques are based on factorization of the time evolution operator using the formula Baker-Campbell-Hausdorff.

[pt] Este trabalho trata do escoamento na escala das gotas e da Reologia de emulsões diluídas. Técnicas analíticas e numéricas são empregadas na solução do problema. Nas vizinhan»cas das gotas o escoamento pode ser considerado livre de efeitos de inércia e conseqüentemente as equações governantes são as equações de Stokes. Esse limite é conhecido na literatura como Microhidrodinâmica. O campo de velocidade e de tensão sobre a superfície das gotas é calculado. Um processo de média espacial é realizado em um volume representativo da suspensão tal que a mesma possa ser estudada como um ruido contínuo equivalente. Métodos assintóticos baseados em aproximações de pequenas deformações das gotas são empregados para produzir teorias de primeira e segunda ordens da razão de viscosidade. Uma extensão da teoria para emulsões diluídas polidispersas é desenvolvida. Uma teoria viscoelástica quasi-linear é construída para emulsões diluídas de alta razão de viscosidade em cisalhamento oscilatório. Em regimes de grandes deformações utiliza-se o Método Integral de Contorno para determinar-se a forma da gota e o campos de velocidade sobre a mesma. O método é descrito em detalhes, tanto do ponto de vista teórico como de sua implementação numérica. A validação da metodologia numérica é feita utilizando resultados teóricos e experimentais, disponíveis na literatura. A reologia da emulsão é estudada em escoamentos de cisalhamento simples, oscilatório, pura extensão e cisalhamento quadrático (escoamento de Poiseuille). Os resultados numéricos para cisalhamento simples são utilizados para determinar constantes materiais da teoria assintótica de segunda ordem para a tensão. Limites não-lineares de escoamento em regimes de razões de viscosidade moderadas para os cisalhamentos simples, oscilatório e quadrático são estudados / [en] This work deals with the flow in the scale of the drops and the Rheology of diluted emulsions. Analytic and numerical techniques are employed in order to solve the problem. In the drop neighborhoods the flow may be considered as free of inertia effects and consequently governed by Stokes equations. In the literature this limit is known as Microhydrodynamics. The flow field and the stress tensor on the drop surface are calculated. A spatial mean process was taken, in a representative suspension volume, in order to study the emulsion as an homogeneous and continuous fluid. Asymptotic methods based in small drop deformation approximation are used to produce first and second orders theories which the parameter is the viscosity ratio. An extension of these theories for polydisperse diluted emulsion is developed. A quasi-linear viscoelasticity theory is constructed for diluted emulsion of high viscosity ratios in oscillatory shear flows. In the regimes of large deformations, the velocity and the stress on the particles are evaluated by a numerical procedure based on the Boundary Integral Method for deformable drops. The theoretical and numerical aspects of the Boundary Integral Method are described in details. The code is validated by comparison the numerical results with the experimental data presented in the literature, and also by comparison with the theoretical results of small deformation. The emulsion rheology is studied in simple shear, oscillatory shear, extensional and also in pressure driven flows. The numerical results are used to determine material constants of the stress theory of the second order. Non linear flow regimes of moderate viscosity ratios in simple shear, oscillatory shear and pressure driven flows are also studied.

O trabalho apresenta uma análise do desempenho de vários métodos de extração de fatores de intensidade de tensão a partir de soluções numéricas obtidas com o método dos elementos finitos generalizados (MEFG). A convergência dos fatores de intensidade de tensão é comparada com a da energia de deformação a fim de investigar a superconvergência dos métodos. Para extração dos fatores de intensidade de tensão e o cálculo da taxa de energia disponibilizada para propagação da fissura, implementam-se os métodos da integral de contorno (MIC), da função cutoff (MFC) e da integral-J no contexto do MEFG. Desenvolve-se a formulação dos métodos de extração de forma a obter uma implementação independente da malha utilizada na modelagem do problema. Aplica-se a extração dos fatores de intensidade de tensão, para modos puros e mistos, em problemas clássicos da mecânica da fratura. Verifica-se a convergência dos fatores de intensidade de tensão e da taxa de energia disponibilizada para a propagação da fissura, obtidos com cada método de extração, com o enriquecimento da ordem polinomial da solução do MEFG. Investiga-se a robustez dos métodos com relação ao tamanho dos domínios de extração / The performance of several techniques to extract stress intensity factors (SIF) from numerical solutions computed with the generalized finite element method (GFEM) is investigated. The convergence of the stress intensity factors is compared with the convergence of strain energy with the aim of investigate the superconvergence of the methods. The contour integral (CIM), the cutoff function (CFM) and the J-integral methods are considered to compute stress intensity factors and energy release rate. The proposed implementation of the extraction techniques is completely independent of the discretization used. Several numerical examples demonstrating the convergence of the computed stress intensity factors and the energy release rate, with the increasing of p order of the GFEM solution, are presented