Дисертації з теми "Method of fundamental solution"
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1
Poullikkas, Andreas. "The Method of Fundamental Solutions for the solution of elliptic boundary value problems." Thesis, Loughborough University, 1997. https://dspace.lboro.ac.uk/2134/27141.
Повний текст джерелаАнотація:
We investigate the use of the Method of Fundamental Solutions (MFS) for the numerical solution of elliptic problems arising in engineering. In particular, we examine harmonic and biharmonic problems with boundary singularities, certain steady-state free boundary flow problems and inhomogeneous problems. The MFS can be viewed as an indirect boundary method with an auxiliary boundary. The solution is approximated by a linear combination of fundamental solutions of the governing equation which are expressed in terms of sources located outside the domain of the problem. The unknown coefficients in the linear combination of fundamental solutions and the location of the sources are determined so that the boundary conditions are satisfied in a least squares sense. The MFS shares the same advantages of the boundary methods over domain discretisation methods. Moreover, it is relatively easy to implement, it is adaptive in the sense that it takes into account sharp changes in the solution and/or in the geometry of the domain and it can easily incorporate complicated boundary conditions.
2
Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.
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Dyhoum, Taysir Emhemed. "The method of fundamental solutions and MCMC methods for solving electrical tomography problems." Thesis, University of Leeds, 2016. http://etheses.whiterose.ac.uk/15552/.
Повний текст джерелаАнотація:
Electrical impedance tomography (EIT) is a non-intrusive and portable imaging technique which has been used widely in many medical, geological and industrial applications for imaging the interior electrical conductivity distribution within a region from the knowledge of the injected currents through attached electrodes and resulting voltages, or boundary potential and current flux. If the quantities involved are all real then EIT is called electrical resistance tomography (ERT). The work in this thesis focuses on solving inverse geometric problems in ERT where we seek detecting the size, the shape and the location of inner objects within a given bounded domain. These ERT problems are governed by Laplace’s equation subject either to the most practical and general boundary conditions, forming the socalled complete-electrode model (CEM), in two dimensions or to the more idealised boundary conditions in three-dimensions called the continuous model. Firstly, the method of the fundamental solutions (MFS) is applied to solve the forward problem of the two-dimensional complete-electrode model of ERT in simplyconnected and multiple-connected domains (rigid inclusion, cavity and composite bimaterial), as well as providing the corresponding MFS solutions for the three-dimensional continuous model. Secondly, a Bayesian approach and the Markov Chain Monte Carlo (MCMC) estimation technique are employed in combinations with the numerical MFS direct solver in order to obtain the inverse solution. The MCMC algorithm is not only used for reconstruction, but it also deals with uncertainty assessment issues. The reliability and accuracy of a fitted object is investigated through some meaningful statistical aspects such as the object boundary histogram and object boundary credible intervals.
4
Bin-Mohsin, Bandar Abdullah. "The method of fundamental solutions for Helmholtz-type problems." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/4843/.
Повний текст джерелаАнотація:
The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations. Inverse problems have become more and more important in various fields of science and technology, and have certainly been one of the fastest growing areas in applied mathematics over the last three decades. However, as inverse geometric problems typically lead to mathematical models which are ill-posed, their solutions are unstable under data perturbations and classical numerical techniques fail to provide accurate and stable solutions.
5
Sedláček, Stanislav. "Aplikace metody hraničních prvků na některé problémy trhliny v blízkosti bi-materiálového rozhraní." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-230134.
Повний текст джерелаАнотація:
There are many shape and other changes in the engineering constructions. These changes cause the concentration of the stress. There is a higher probability of the crack initiation in the vicinity of these stress concentrators. The problems of the crack can be solved nowadays only with help of sufficient numeric tools. The Boundary Element Method is one of the many numerical tools which offer the solution of some problems of the mechanics. The goal of this diploma thesis is to formulate boundary element method for the plane problem of the linear elasticity for izotropic material with different types of the stress concentrators.
6
Bozkaya, Canan. "Boundary Element Method Solution Of Initial And Boundary Value Problems In Fluid Dynamics And Magnetohydrodynamics." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609552/index.pdf.
Повний текст джерелаАнотація:
In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M.
For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.
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Sun, Liecheng. "ANALYTICAL STRIP METHOD TO ANTISYMMETRIC LAMINATED PLATES." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/715.
Повний текст джерелаАнотація:
An Analytical Strip Method (ASM) for the analysis of stiffened and non-stiffened antisymmetric laminated composite plates is derived by considering the bending-extension coupling effect for bending, free vibration and buckling. A system of three equations of equilibrium, governing the general response of arbitrarily laminated composite plates, is reduced to a single eighth order partial differential equation in terms of a displacement function. The displacement function is solved in a single series form to determine the displacement, fundamental frequency, and buckling load of antisymmetric cross-ply and angle-ply laminated composite plates. The solution is applicable to rectangular plates with two opposite edges simply supported, while the other edges are simply supported, clamped, free, beam supported, or any combinations of these boundary conditions.
This method overcomes the limitations of other analytical methods (Navier’s and Lévy’s), and provides an alternative to numerical, semi-numerical, and approximate methods of analysis. Numerical examples of bending, free vibration, and buckling of antisymmetric laminated composite plates are presented in tabular and graphical form. Whenever possible, the results of the present study are compared with those published in the literature and/or ANSYS solutions. The comparison firmly establishes that this method could be used for the analysis of antisymmetric laminated composite plates. Future research needs are identified for the aspects that have not been reached by the present study and others.
8
Reeve, Thomas Henry. "The method of fundamental solutions for some direct and inverse problems." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4278/.
Повний текст джерелаАнотація:
We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used.
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Bozkaya, Nuray. "Application Of The Boundary Element Method To Parabolic Type Equations." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12612074/index.pdf.
Повний текст джерелаАнотація:
In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis.
Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear's scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.
10
Pesce, Antonello. "Stochastic fundamental solutions for a class of degenerate SPDEs." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14559/.
Повний текст джерелаАнотація:
In this thesis, we look for a fundamental solution for a broad, possibly degenerate class of stochastic partial differential equations (SPDEs), whose deterministic part is a Kolmogorov equation with coefficients measurable in the time variable. We use a version of the It\^o-Wentzell formula to reduce the SPDE to a PDE, for which we extend the classic Levi's parametrix method to find a fundamental solution.
11
Hakim, Souheil. "Scatter analysis using the method of fundamental solutions with applications to the sheep fetal lung." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=19651.
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The method of fundamental solutions (MFS) is a boundary method applied to predict the geometric properties of acoustic scatterers present in a soft biological medium by modeling the medium as a randomized volume distribution of small bodies of any size and shape suspended in a fluid medium and insonified by a short pulse. MFS-based scattering techniques are derived and used to estimate scattering from non-spherical sources in Rayleigh-range as well as medium-range frequencies. The validity of the MFS is investigated by characterizing scattering from bodies of known geometry such as spheres using MFS-based techniques and comparing results to those obtained using known spherical correlation methods derived analytically. Both techniques are in good agreement. Thus, MFS-based techniques account for all types of scatterers beyond particles where solutions are limited to particle shape for which a Laplace's equation is separable. Random media with different structural properties are used to simulate fetal lamb lung parenchyma. The size and shape of tissue microscopic constituents are estimated from an analysis of the radio frequency echo signal power spectrum. Correlation functions are used to model backscatter from spherical as well as non-spherical bodies. The relationship between the backscattered power spectrum and the medium correlation function is expressed in terms of an acoustic form factor model which describes the size and shape properties of the acoustic scatterers present in the medium. Numerical results demonstrate that the form factor models vary with the size and shape of the scatterers. Using these methods it is possible to assess the effect of bodies not perfectly spherical (spheroids) present in a sample tissue on the estimation of the size of scatterers. If spheroidal bodies are present in the medium, the spherical correlation model overestimates or underestimates the size of scatterers. This is what has been observed in the lamb fetal lung. This implies that the spherical correlation model may not be sufficient to predict backscatter accurately in media containing not perfectly spherical bodies. These numerical studies have provided insight into bulk scattering from non-spherical bodies using simple and fast numerical techniques in comparison to Finite Element Methods (FEM) and Boundary Element Methods (BEM) techniques used to solved the scattering problem.
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Pieronek, Lukas [Verfasser], and Andreas [Gutachter] Kleefeld. "The method of fundamental solutions for computing interior transmission eigenvalues / Lukas Pieronek ; Gutachter: Andreas Kleefeld." Cottbus : BTU Cottbus - Senftenberg, 2020. http://d-nb.info/1218080167/34.
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Passos, José Jarbson Salustiano dos. "Análise da estabilidade estatíca e dinâmica de vigas pelo método dos elementos de contorno." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/5387.
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In this work new solutions based on the direct Boundary Element Method (BEM) for static and dynamic stability beam problems are presented. Both Euler-Bernoulli and Timoshenko models are used to represent the beam responses. All discussions on mathematical steps to write down the BEM representation are presented. Alternative fundamental solutions for static and dynamic Euler-Bernoulli beam stability problems are proposed, resulting in the simpler forms than conventional fundamental solutions commonly used for the problems. In addition, the effects of Pasternak elastic foundations are incorporated into the expressions of proposed fundamental solutions. For the case of the Timoshenko static and dinamic stability, all the direct BEM representation (integral equations, fundamental solutions and algebraic equations) here proposed are inovative. Their fundamental solutions incorporate Pasternak foundation effects as well. A convenient strategy is also presented in order to deal with elastic end supports and discontinuities at beam domain such as abrupt change of cross section geometry (stepped beams), internetiated axial load, rigid or elastic supports at beam domain. Numerical examples incorporating various types of boundary conditions and domain discontinuities in order to validate the proposed BEM solution are presented.
Neste trabalho, novas soluções, baseadas no Método dos Elementos de Contorno (MEC) direto, são apresentadas para os problemas de estabilidade estática e dinâmica de vigas. Ambos modelos de Euler-Bernoulli e Timoshenko são usados para representar as respostas da viga. Todas as discussões sobre os passos matemáticos para escrever a representação do MEC são apresentadas. Soluções fundamentais alternativas são propostas para o problema da estabilidade estática e dinâmica de vigas de Euler-Bernoulli, resultando em formas mais simples que as comumente usadas para esses problemas. Além disso, os efeitos de fundações elásticas de Pasternak são incorporadas nas expressões das soluções fundamentais propostas. Para o caso da estabilidade estática e dinâmica de Timoshenko, toda a representação do MEC (equações integrais, soluções fundamentais e equações algébricas) aqui proposta é inovadora. Suas soluções fundamentais incorporam os efeitos da base elástica de Pasternak também. Uma estratégia conveniente é também apresentada para lidar com apoios elásticos no contorno e com discontinuidades no domínio tais como: mudança abrupta de geometria da seção transversal (viga escalonada), carga axial intermediária, apoios rígidos ou elásticos no domínio. Exemplos numéricos incorporando vários tipos de condições de contorno e discontinuidades no domínio são apresentadas para validar as soluções do MEC propostas.
14
Zhao, Yanfei. "Fundamental Solutions and Numerical Modeling of Internal and Interfacial Defects in Magneto-Electro-Elastic Bi-Materials." University of Akron / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1433529049.
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Maia, Cibelle Dias de Carvalho Dantas. "Flexão e estabilidade de barras usando o modelo de Bickford-Reddy: uma abordagem pelo método dos elementos de contorno." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9110.
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In this work, new solutions based on the Boundary Element Method (BEM) are established for the linear analysis of bending and stability problems of Reddy-Bickford beams. All mathematical steps to write the BEM representation are properly presented: transformation of governing differential equations into equivalent integral equations, deduction of fundamental solutions, formation and solution of algebraic representation.In addition, elastic foundations (winkler and pasternak’s types) attached to Reddy-Bickford beams are solved by BEM as well. It is also addressed a convenient strategy for discontinuities in the area such as abrupt change in geometry of the cross section (stepped beam), intermediate axial load, intermediate supports (continuous beam). Numerical examples incorporating various types of discontinuities and boundary conditions in the field are presented to validate the solutions proposed BEM.
Neste trabalho, novas soluções, baseadas no Método dos Elementos de Contorno (MEC), são estabelecidas para a análise linear de problemas de flexão e estabilidade de barras de Bickford-Reddy. Todos os passos matemáticos para estabelecer a representação do MEC são apresentados: transformações das equações diferenciais governantes em equações integrais equivalentes, dedução das soluções fundamentais, obtenção e solução do sistema alébrico. Além disso, fundações elásticas (Winkler e Pasternak) em barras de Bickford-Reddy também são analisados pelo MEC. É também abordada uma conveniente estratégia para de discontinuidades no domínio tais como: mudança abrupta de geometria da seção transversal (viga escalonada), carga axial intermediária, apoios rígidos no domínio (viga contínua). Exemplos numéricos incorporando vários tipos de condições de contorno e discontinuidades no domínio são apresentadas para validar as soluções do MEC propostas.
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Bisenius, Sellgren Kajsa. "En studie om elevers val av metoder vid subtraktionsberäkningar." Thesis, Södertörn University College, Lärarutbildningen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:sh:diva-3407.
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In this qualitative study of students’ methods of calculating subtractions, I have used interviews, subtraction exercises and analysis of teaching material. The purpose of my study was to explore which methods students in grade three uses when calculating subtractions. I also wanted to highlight which strategies the students use and their comprehension of the concept of subtraction. In the study, I also highlight the different pedagogical ideas on which the teaching material is based on and the students’ choice of methods. The study shows that the students choose to use the methods”deduct” and “kind of number” independently. Further it also shows that the students choose to switch from the method “deduct” to “kind of number” when the numbers in the exercises are further up on the number axis. When asked, the students answered that subtraction means “minus” which they in turn explained as removing something, an explanation confirmed by the Swedish Academy dictionary. The students’ choice of methods and teaching material is based on different fundamental pedagogical view.
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Tran, Anh-Tuan. "Modélisation et simulation des interfaces non classiques dans l’écoulement de Stokes et dans les composites élastiques fibreux." Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1071/document.
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Ce travail de thèse, constitué de deux parties apparemment très différentes, a pour objectif commun de modéliser et simuler certaines interfaces non classiques en mécanique des fluides et en mécanique des solides. Dans la première partie qu'est la partie principale du travail, l'écoulement de Stokes d'un fluide dans un canal encadré par deux parois solides parallèles est étudié. La surface d'une paroi étant supposée lisse, la condition d'adhérence parfaite classique est adoptée pour l'interface fluide-solide homogène correspondante. La surface de l'autre paroi étant supposée rugueuse et capable de piéger de petites poches d'air, l'interface liquide-solide correspondante est donc hétérogène. La première partie de ce travail consiste à homogénéiser l'interface liquide-solide hétérogène de façon à remplacer cette dernière par une interface fluide-solide homogène imparfaite caractérisée par une longueur de glissement effective. Le problème essentiel de déterminer la longueur de glissement effective est résolu par le développement : (i) d'une approche semi-analytique dans le cas où la surface rugueuse est périodique; (ii) d'une approche basée sur la méthode de solution fondamentale dans le cas où la surface rugueuse est aléatoire. Les résultats obtenus par les approches développées sont systématiquement comparés avec ceux délivrés par la méthode des éléments finis. La deuxième partie du travail est de déterminer les modules élastiques effectifs d'un composite fibreux dans lequel les interfaces entre la matrice et les fibres sont imparfaites et décrites par le modèle membranaire. Une méthode numérique efficace basée sur la transformée de Fourier est ainsi développée et implantée pour traiter le cas général où la section d'une fibre peut avoir une forme quelconqueThe present work, consisting of two seemingly very different parties, aims at modeling and simulating some non-classical interfaces in fluid mechanics and solid mechanics. In the first part which is the main part of the work, the Stokes flow of a fluid in a channel bounded by two parallel solid walls is studied. The surface of a solid wall being assumed to be smooth, the classic perfect adherence condition is adopted for the corresponding homogeneous fluid-solid interface. The surface of the other wall being taken to be rough and capable of trapping small pockets of air, the corresponding liquid-solid interface is heterogeneous. The first part of this work is to homogenize the heterogeneous liquid-solid interface so as to replace it by an imperfect homogeneous fluid-solid interface characterized by an effective slip length. The essential underlying problem of determining the effective slip length is achieved by developing: (i) a semi-analytical approach when the rough surface is periodic; (ii) an approach based on the fundamental solution method when the surface is randomly rough. The results obtained by the developed approaches are systematically compared with those issued from the finite element method. The second part of the work is to determine the effective elastic moduli of a fiber composite in which the interfaces between the matrix and fibers are imperfect and described by the membrane model. An efficient numerical method based on the fast Fourier transform is developed and implemented to treat the general case where the section of a fiber can be of any shape
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Hanahata, H. "Fundamental analysis of production methods for polyurethaneureas : Kinetics studies of the formation of polyurethaneureas in solution and the construction and evaluation of deterministic and stochastic computer models for real-time computer-control." Thesis, University of Bradford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384273.
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Zhao, Shunliu. "Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1247718304.
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Caille, Laetitia. "Méthodes de régularisation évanescente pour la complétion de données." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC231/document.
Повний текст джерелаАнотація:
Les problèmes de complétion de données interviennent dans divers domaines de la physique, tels que la mécanique, l'acoustique ou la thermique. La mesure directe des conditions aux limites se heurte souvent à l'impossibilité de placer l'instrumentation adéquate. La détermination de ces données n'est alors possible que grâce à des informations complémentaires. Des mesures surabondantes sur une partie accessible de la frontière mènent à la résolution d'un problème inverse de type Cauchy. Cependant, dans certains cas, des mesures directes sur la frontière sont irréalisables, des mesures de champs plus facilement accessibles permettent de pallier ce problème. Cette thèse présente des méthodes de régularisation évanescente qui permettent de trouver, parmi toutes les solutions de l'équation d'équilibre, la solution du problème de complétion de données qui s'approche au mieux des données de type Cauchy ou de champs partiels. Ces processus itératifs ne dépendent pas d'un coefficient de régularisation et sont robustes vis à vis du bruit sur les données, qui sont recalculées et de ce fait débruitées. Nous nous intéressons, dans un premier temps, à la résolution de problèmes de Cauchy associés à l'équation d'Helmholtz. Une étude numérique complète est menée, en utilisant la méthode des solutions fondamentales en tant que méthode numérique pour discrétiser l'espace des solutions de l'équation d'Helmholtz. Des reconstructions précises attestent de l'efficacité et de la robustesse de la méthode. Nous présentons, dans un second temps, la généralisation de la méthode de régularisation évanescente aux problèmes de complétion de données à partir de mesures de champs partielles. Des simulations numériques, pour l'opérateur de Lamé, dans le cadre des éléments finis et des solutions fondamentales, montrent la capacité de la méthode à compléter et débruiter des données partielles de champs de déplacements et à identifier les conditions aux limites en tout point de la frontière. Nous retrouvons des reconstructions précises et un débruitage efficace des données lorsque l'algorithme est appliqué à des mesures réelles issues de corrélation d'images numériques. Un éventuel changement de comportement du matériau est détecté grâce à l'analyse des résidus de déplacementsData completion problems occur in many engineering fields, such as mechanical, acoustical and thermal sciences. Direct measurement of boundary conditions is often confronting with the impossibility of placing the appropriate instrumentation. The determination of these data is then possible only through additional informations. Overprescribed measurements on an accessible part of the boundary lead to the resolution of an inverse Cauchy problem. However, in some cases, direct measurements on the boundary are inaccessible, to overcome this problem field measurements are more easily accessible. This thesis presents fading regularization methods that allow to find, among all the solutions of the equilibrium equation, the solution of the data completion problem which fits at best Cauchy or partial fields data. These iterative processesdo not depend on a regularization coefficient and are robust with respect to the noise on the data, which are recomputed and therefore denoised. We are interested initially in solving Cauchy problems associated with the Helmholtz equation. A complete numerical study is made, usingthe method of fundamental solutions as a numerical method for discretizing the space of the Helmholtz equation solutions. Accurate reconstructions attest to the efficiency and the robustness of the method. We present, in a second time, the generalization of the fading regularization method to the data completion problems from partial full-field measurements. Numerical simulations, for the Lamé operator, using the finite element method or the method of fundamental solutions, show the ability of the iterative process to complete and denoise partial displacements fields data and to identify the boundary conditions at any point. We find precise reconstructions and efficient denoising of the data when the algorithm is applied to real measurements from digital image correlation. A possible change in the material behavior is detected thanks to the analysis of the displacements residuals
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Perez, Mario Mourelle. "Use of isotropic fundamental solutions for solving anisotropic problems." Thesis, University of Portsmouth, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335756.
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Maghoul, Pooneh. "Solutions fondamentales en Géo-Poro-Mécanique multiphasique pour l'analyse des effets de site sismiques." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00599397.
Повний текст джерелаАнотація:
Ce travail de recherche se situe dans le cadre du développement de la méthode des éléments de frontière (BEM) pour les milieux poreux multiphasiques. À l'heure actuelle, l'application de la BEM aux pr oblèmes des milieux poreux non-saturés est encore limitée, car l'expression analytique exacte de la solution fondamentale n'a pas été obtenue, ni dans le domaine transformé ni dans le domaine réel. Ceci provient de la complexité du système d'équations régissant le comportement des milieux poreux non-saturés. Les développements de la BEM pour les sols non-saturés effectués au cours de cette thèse sont basés sur les modèles thermo-hydro-mécanique (THHM) et hydro-mécanique (HHM) présentés dans la première partie de ce mémoire. Ces modèles phénoménologiques basés sur la théorie de la poromécanique et les acquis expérimentaux sont obtenus dans le cadre du modèle mathématique présenté par Gatmiri (1997) et Gatmiri et al. (1998). Après avoir présenté les modèles THHM et HHM, on établit pour la première fois les équations intégrales de frontière et les solutions fondamentales associées pour un milieu poreux non-saturé sous chargement quasi-statique pour les deux cas isotherme (2D dans le domaine de Laplace) et non-isotherme (2D et 3D dans les domaines de Laplace et temporel). Aussi, les équations intégrales de frontière ainsi que les solutions fondamentales 2D et 3D (dans le domaine de Laplace) pour le modèle dynamique couplé des sols non-saturés sont obtenues. Ensuite, les formulations d'éléments de frontière (BEM) basées sur la méthode quadrature de convolution (MQC) concernant les milieux poreux saturé et non-saturé sous chargement quasi-statique isotherme et dynamique sont implémentées dans le code de calcul " HYBRID ". Ayant intégrées les formulations de BEM pour les problèmes de propagation d'ondes ainsi que pour les problèmes de consolidation dans les milieux poreux saturés et non-saturés, il semble que nous ayons fourni à l'heure actuelle le premier code de calcul aux éléments de frontière (BEM) qui modélise les différents problèmes dans les sols secs, saturés et non-saturés. Une fois le code vérifié et validé, des études paramétriques portant sur des effets de site sismiques sont effectuées. Le but recherché est d'aboutir à un critère simple, directement exploitable par les ingénieurs, combinant les caractéristiques géométriques et les caractéristiques du sol, permettant de prédire l'amplification du spectre de réponse en accélération dans des vallées sédimentaires aussi bien que vides
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Han, Qi. "Electrocatalysis at the Electrode-Adsorbate-Solution Interface: Fundamental Studies." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1574855036013662.
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Chen, Li. "A Nonlinear Ship Wave Solution Method." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/td/1727.
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Tekin, Íbrahim. "Moment method solution for junction problems /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487948807586872.
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Kularathna, Shyamini. "Splitting solution scheme for material point method." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274140.
Повний текст джерелаАнотація:
Material point method (MPM) is a numerical tool which was originally used for modelling large deformations of solid mechanics problems. Due to the particle based spatial discretiza- tion, MPM is naturally capable of handling large mass movements together with topological changes. Further, the Lagrangian particles in MPM allow an easy implementation of history dependent materials. So far, however, research on MPM has been mostly restricted to explicit dynamic formu- lations with linear approximation functions. This is because of the simplicity and the low computational cost of such explicit algorithms. Particularly in MPM analysis of geomechan- ics problems, a considerable attention is given to the standard explicit formulation to model dynamic large deformations of geomaterials. Nonetheless, several limitations exist. In the limit of incompressibility, a significantly small time step is required to ensure the stability of the explicit formulation. Time step size restriction is also present in low permeability cases in porous media analysis. Spurious pressure oscillations are another numerical instability present in nearly incompressible flow behaviours. This research considers an implicit treatment of the pressure in MPM algorithm to simu- late material incompressibility. The coupled velocity (v)-pressure (p) governing equations are solved by applying Chorin’s projection method which exhibits an inherent pressure stability. Hence, linear finite elements can be used in the MPM solver. The main purpose of this new MPM formulation is to mitigate artificial pressure oscillations and time step restrictions present in the explicit MPM approach. First, a single phase MPM solver is applied to free surface incompressible fluid flow problems. Numerical results show a better approximation of the pressure field compared to the results obtained from the explicit MPM. The proposed formulation is then extended to model fully saturated porous materials with incompress- ible constituents. A solid velocity(v S )-fluid velocity (v F )-pore pressure (p) formulation is presented within the framework of mixture theory. Comparing the numerical results for the one-dimensional consolidation problem shows that the proposed incompressible MPM algorithm provides a stable and accurate pore pressure field even without implementing damping in the solver. Finally, the coupled MPM is used to solve a two-dimensional wave propagation problem and a plain strain consolidation problem. One of the important features of the proposed hydro mechanical coupled MPM formulation is that the time step size is not dependent on the incompressibility and the permeability of the porous medium.
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Temiño, Gutiérrez Inés. "Solution-processed organic field-effect transistors: from fundamental aspects to applications." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/669373.
Повний текст джерелаАнотація:
En esta tesis hemos estudiado varios factores relacionados con los transistores orgánicos de efecto campo (OFETs) procesados por solución, incluyendo su fabricación, su caracterización eléctrica y posibles aplicaciones, especialmente en el campo de sensores físicos. En este trabajo se han utilizado principalmente disoluciones de diferentes semiconductores orgánicos (OSC) de pequeña molécula tipo-p y polímeros aislantes. La deposición de estas mezclas para obtener las capas activas de los OFETs se ha llevado a cabo mediante una técnica de procesado por solución escalable, en concreto la denominada bar-assisted meniscus shearing (BAMS). El propósito principal de este trabajo ha sido comprender la influencia que tienen los parámetros de fabricación elegidos sobre las propiedades morfológicas y estructurales de las capas activas resultantes, y, por tanto, su impacto en las propiedades eléctricas de los dispositivos finales. Se ha realizado un estudio detallado a escala nanométrica de capas basadas en OSC:polímero aislante, descifrando la separación vertical de ambos componentes y el efecto que tiene sobre la estabilidad y el rendimiento de los dispositivos. Además, se han explorado diferentes métodos de dopaje con el objetivo de mejorar las características eléctricas de los OFETs que sufren de una alta resistencia de contacto. También se ha estudiado la relación entre propiedades morfológicas y eléctricas empleando dispositivos flexibles sometidos a tensión mecánica. Finalmente, gracias a la optimización de los parámetros de procesado se han fabricado OFETs con una alta sensibilidad a radiación de rayos-X, explicando a su vez cómo la morfología y el transporte de carga en la capa activa determinan la respuesta de estos dispositivos.In this thesis we have studied several aspects related to organic field-effect transistors (OFETs) printed from solution, including their fabrication, their electrical characterisation, and further applications, especially in the field of physical sensing. Blends of different p‑type small molecule organic semiconductors (OSCs) and insulating polymer binders have been employed in this research work. For the deposition of such blends as active layers for OFETs a scalable solution processing technique has been exploited, namely bar‑assisted meniscus shearing (BAMS). The main purpose of the work carried out has been understanding the influence of the fabrication parameters of choice on the morphological and structural features of the resulting active layer and, thus, their impact on the electrical performance of the final devices. A detailed nanoscale study of OSC:insulating polymer thin films has been conducted, elucidating the vertical stratification of both components and its effect on the devices stability and performance. Further, aiming at improving the electrical characteristics of devices exhibiting high contact resistance values, different doping methodologies have been explored. In addition, the morphology-performance relationship has been studied for flexible OFET devices subjected to mechanical strain. Finally, OFETs exhibiting high sensitivity to X-ray radiation have been fabricated by optimising the processing parameters, rationalising how the morphological and transport properties of the active layer determine the sensing capability of such devices.
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Omeragić, Dževat. "Differentiation of finite element approximations based on fundamental solution of B.V.P." Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41738.
Повний текст джерелаАнотація:
In this thesis a method based on Green's second identity is developed for computing several orders of derivatives from finite element solutions with $C sp circ$ continuity. The integration by parts implicit in Green's theorem permits numerical integration to replace numerical differentiation. This procedure is initially developed for harmonic functions, then extended to Poisson and Helmholtz equations for a circular region, as well as to harmonic potentials in axi-symmetric coordinates. For the 2-D Laplace operator three other base regions have been introduced: rectangle, sector of circle and sector of ring. The method is numerically stable, position independent and very accurate. Its accuracy is the same as of original finite element solution or even better, when the point of interest is not close to the edge of the region. Treatment of singular integrals is based on using the finite part integration concept. Integration formulas are given. The method is verified with analytical functions, using accurate values and finite element solutions. It is also applied in anisotropic nonlinear magnetic material modeling.Accurate computation of derivatives from finite element solutions is an important step in CAD postprocessing. Direct differentiation of basis functions is inaccurate. Superconvergent methods give satisfactory results in gradient calculation, but their accuracy is position dependent and second or higher derivatives are unreliable. With the new technique it is possible to compute derivatives even where finite element solution itself has insufficient continuity, e.g. finding second order derivatives from $C sp circ$ continuous solutions.
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Cayan, Fatma Nihan. "The Method Of Lines Solution Of Discrete Ordinates Method For Nongray Media." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607401/index.pdf.
Повний текст джерелаАнотація:
A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for the prediction of radiative heat transfer in nongray absorbing-emitting media was developed by incorporation of two different gas spectral radiative property models, namely wide band correlated-k (WBCK) and spectral line-based weighted sum of gray gases (SLW) models.
Predictive accuracy and computational efficiency of the developed code were assessed by applying it to the predictions of source term distributions and net wall radiative heat fluxes in several one- and two-dimensional test problems including isothermal/non-isothermal and homogeneous/non-homogeneous media of water vapor, carbon dioxide or mixture of both, and benchmarking its steady-state predictions against line-by-line (LBL) solutions and measurements available in the literature. In order to demonstrate the improvements brought about by these two spectral models over and above the ones obtained by gray gas approximation, predictions obtained by these spectral models were also compared with those of gray gas model. Comparisons reveal that MOL solution of DOM with SLW model produces the most accurate results for radiative heat fluxes and source terms at the expense of computation time when compared with MOL solution of DOM with WBCK and gray gas models.
In an attempt to gain an insight into the conditions under which the source term predictions obtained with gray gas model produce acceptable accuracy for engineering applications when compared with those of gas spectral radiative property models, a parametric study was also performed. Comparisons reveal reasonable agreement for problems containing low concentration of absorbing-emitting media at low temperatures.
Overall evaluation of the performance of the radiation code developed in this study points out that it provides accurate solutions with SLW model and can be used with confidence in conjunction with computational fluid dynamics (CFD) codes based on the same approach.
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梁耀華 and Yew-wah Leung. "Finite element solution on microcomputers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1989. http://hub.hku.hk/bib/B31209300.
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Leung, Yew-wah. "Finite element solution on microcomputers /." [Hong Kong] : University of Hong Kong, 1989. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12754948.
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Enmark, Martin. "Fundamental Investigations of Supercritical Fluid Chromatography." Doctoral thesis, Karlstads universitet, Institutionen för ingenjörs- och kemivetenskaper, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-37913.
Повний текст джерелаАнотація:
This thesis aims at a deeper understanding of Supercritical Fluid Chromatography (SFC). Although preparative SFC has started to replace Liquid Chromatography (LC) in the pharmaceutical industry - because of its advantages in speed and its less environmental impact - fundamental understanding is still lacking. Therefore there is no rigid framework to characterize adsorption or to understand the impact of changes in operational conditions. In Paper I we demonstrated, after careful system verification, that most methods applied to determine adsorption isotherms in LC could not be applied directly in SFC. This was mainly due to operational differences and to the fact that the fluid is compressible which means that everything considered constant in LC varies in SFC. In Paper II we showed that the most accurate methods for adsorption isotherm determination in LC, the so called plateau methods, do not work properly for SFC. Instead, methods based on overloaded profiles should be preferred. In Paper III a Design of Experiments approach was successfully used to quantitatively describe the retention behavior of several solutes and the productivity of a two component separation system. This approach can be used to optimize SFC separations or to provide information about the separation system. In Paper IV severe peak distortion effects, suspected to arise from injection solvent and mobile phase fluid mismatches, were carefully investigated using experiments and simulations. By this approach it was possible to examine the underlying reasons for the distortions, which is vital for method development. Finally, in Paper V, the acquired knowledge from Paper I-IV was used to perform reliable scale-up in an industrial setting for the first time. This was done by carefully matching the conditions inside the analytical and preparative column with each other. The results could therefore provide the industry with key knowledge for further implementation of SFC.This thesis aims at a deeper understanding of Supercritical Fluid Chromatography (SFC). Although preparative SFC has started to replace Liquid Chromatography (LC) in the pharmaceutical industry - because of its advantages in speed and its less environmental impact - fundamental understanding is still lacking. Therefore there is no rigid framework to characterize adsorption or to understand the impact of changes in operational conditions. In Paper I-II it was demonstrated why most methods applied to determine adsorption isotherms in LC could not be applied directly for SFC. Methods based on extracting data from overloaded profiles should be preferred. In Paper III a Design of Experiments approach was successfully used to quantitatively describe the behavior of several solutes in a separation system. This approach can be used to optimize SFC separations or to provide information about the separation system. In Paper IV severe peak distortion effects often observed in SFC were carefully investigated and explained using experiments and simulations. Finally, in Paper V, the prerequisites for performing reliable and predictable scale-up of SFC were investigated by small and large scale experiments.
Paper 4 ("Evaluation of scale-up from analytical to preparative...") ingick som manuskript med samma titel i avhandlingen. Nu publicerad.
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Kurus, Gulay. "Solution Of Helmholtz Type Equations By Differential Quadarature Method." Master's thesis, METU, 2000. http://etd.lib.metu.edu.tr/upload/2/12605383/index.pdf.
Повний текст джерелаАнотація:
This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
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René, Alexandre. "Spectral Solution Method for Distributed Delay Stochastic Differential Equations." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34327.
Повний текст джерелаАнотація:
Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be useful for a wider variety of cases than those we have considered. We show how it can be used to map the distributed delay equation to a known multivariate system, and obtain expressions for the system's time-dependent mean and autocovariance. These are in the form of series over the system's natural modes and completely define the solution. — An interpretation of the system as an amplitude process is explored. We show that for a wide range of realistic parameters, dynamics are dominated by only a few modes, implying that most of the observed behaviour of stochastic delayed equations is constrained to a low-dimensional subspace. — The expression for the autocovariance is given particular attention. A recurring problem for stochastic delay equations is the description of their temporal structure. We show that the series expression for the autocovariance does converge over a meaningful range of time lags, and therefore provides a means of describing this temporal structure.
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BATISTA, SILVIO ROGERIO DE FREITAS. "ENERGY METHOD FOR SOLUTION OF INELASTIC TRUSSES WITH DAMAGE." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1994. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33260@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORUNIVERSIDADE FEDERAL DO MARANHÃO
O presente trabalho apresenta uma generalização do teorema de Castigliano para a análise quase-estática de treliças inelásticas com dano (elasto-plásticas e elasto-viscoplásticas). É desenvolvida uma formulação abstrata geral para o problema considerando-se qualquer tipo de teoria constitutiva com variáveis internas. Uma técnica de aproximação numérica é apresentada, com base na decomposição aditiva do operador, e um algoritmo de solução é proposto. Finalmente a teoria proposta é testada simulando-se a ruptura de treliças metálicas submetidas a carregamentos monótonos e cíclicos (fadiga).
The present work is concerned with an extension of the Castigliano s theorem to the case of inelastic damageable trusses (elasto-plastic and elasto-viscoplastic behavior). A general formulation that takes into account any kind of constitutive theory with internal variables is presented. A numerical technique, based on the operator splitting method, for approximating the resulting equations is proposed. Finally, the proposed theory is checked through examples concerning cyclic and monotone loadings in metallic trusses.
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Poole, Mark W. "Numerical solution of an electropaint problem." Thesis, Cranfield University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309789.
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RIBEIRO, THIAGO DA SILVA. "FUNDAMENTAL ASPECTS OF BORON REMOVAL FROM WASTEWATERS BY ELECTROCOAGULATION METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=36398@1.
Повний текст джерелаАнотація:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
BOLSA NOTA 10
Compostos de boro são utilizados na indústria metalúrgica, microeletrônica, de vidros, na agricultura, etc. Esse elemento é um micronutriente essencial no desenvolvimento de microrganismos, plantas, animais e humanos. No entanto, pode ser tóxico em grandes concentrações e por isso necessita ser removido de águas e efluentes. No Brasil, o limite padrão é de 0,5mg/L para águas doces de classe I e II, estabelecido pela resolução do Conama 357/2005. Por sua vez, a resolução do Conama 430/2011 estabelece um padrão de lançamento de efluentes de 5mg/L. A presente dissertação tem como objetivo geral estudar a remoção de boro por eletrocoagulação para o tratamento de águas e efluentes contendo boro, utilizando uma célula com um arranjo de 4 eletrodos de alumínio (2 catodos e 2 anodos) monopolares em paralelo. Os resultados obtidos mostram que o processo de eletrocoagulação é uma alternativa viável para a remoção de boro, e alcança eficiências em torno de 70 por cento (em pH inicial igual à 4; densidade de corrente igual à 18,75mA/cm2 e tempo de eletrólise igual à 90min). O modelo cinético que melhor descreve a remoção de boro foi o de pseudo-primeira ordem. O modelo de Langmuir se ajustou muito bem aos dados experimentais obtidos. O valor de qm obtido pelo modelo de Langmuir refletiu a elevada capacidade de adsorção máxima (qm é igual à 334mg/g). Através das análises por Microscopia Eletrônica de Varredura (MEV) e por Espectroscopia de Energia Dispersiva (EDS) na superfície dos eletrodos, observou-se a presença de corrosão do tipo localizada nos catodos e a corrosão do tipo uniforme nos anodos. A morfologia do lodo produzido no processo de eletrocoagulação foi analisada por MEV, indicando a presença de uma morfologia heterogênea na superfície, enquanto que a análise por Difração de Raios-X (DRX) apresentou picos largos característicos de um material amorfo e a fase de alumínio predominante foi a boehmita, AlO(OH), finalmente, através da análise por Espectroscopia por Perda de Energia de Elétrons (EELS) foi possível a detecção do boro no lodo, além da detecção de alumínio e de oxigênio. Diante dos resultados obtidos no estudo de otimização a partir da Metodologia de Superfície de Resposta (RSM) constatou-se que o desenvolvimento de um modelo matemático por análise de regressão possibilitou a avaliação do efeito das variáveis independentes (densidade de corrente, pH inicial e tempo de eletrólise) e as suas interações na remoção de boro.
Boron compounds are used in the metallurgical industry, microelectronics, glassware, agriculture, etc. This element is an essential micronutrient in the development of microorganisms, plants, animals and humans. However, it can be toxic in high concentrations and therefore needs to be removed from water and effluent. In Brazil, the standard limit is 0.5mg/L for Class I and II freshwaters, established by Conama Resolution 357/2005. In turn, the Conama 430/2011 resolution establishes an effluent discharge standard of 5mg/L. The present dissertation aims to study the removal of boron by electrocoagulation for the treatment of water and effluents containing boron, using a cell with an arrangement of 4 monopolar aluminum electrodes (2 cathodes and 2 anodes) in parallel. The results show that the electrocoagulation process is a viable alternative for the removal of boron and reaches efficiencies around 70 per cent (at initial pH equals to 4, current density equals to 18.75mA/cm2 and electrolysis time equals to 90min). The kinetic model that best describes the removal of boron was pseudo-first order. The Langmuir model fitted very well to the experimental data obtained. The value of qm obtained by the Langmuir model reflected the high maximum adsorption capacity (qm equals to 334mg/g). Through the analysis by Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) on the surface of the electrodes, it was observed the presence of pitting corrosion in the cathodes and uniform corrosion in the anodes. The morphology of the sludge produced in the electrocoagulation process was analyzed by SEM, indicating the presence of a heterogeneous surface morphology, while the X-ray diffraction (XRD) analysis showed broad peaks characteristic of an amorphous material and the predominant aluminum phase was boehmite, AlO(OH), finally, through the Electron Energy Loss Spectroscopy (EELS) analysis, it was possible to detect boron in the sludge, as well as aluminum and oxygen. In view of the results obtained in the optimization study from the Response Surface Methodology (RSM), it was verified that the development of a mathematical model by regression analysis made possible the evaluation of the effect of the independent variables (current density, initial pH and time of electrolysis) and their interactions in the removal of boron.
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Jamal, Dany. "Solution methods of composite beams." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2012. http://www.nusl.cz/ntk/nusl-264913.
Повний текст джерелаАнотація:
Solutions of composite beams encounter some specific problems, such as shrinkage and creep of concrete, cracking of concrete and plasticity of steel, partial interaction of elements or history of erection and loading process. These factors and others affect the distribution of internal forces along the beam, the distribution of stresses along the cross-section and also stiffness and deflection of beams. The goal is to describe and compare methods for analysis of composite steel and concrete beams by more simplified approaches allowed by Eurocode with more advanced techniques. The studies will be carried out on the simply supported and continuous beams designed with respect to Eurocode 1, 2, 3 and 4.
39
Bircan, Ali. "Solution Of Inverse Electrocardiography Problem Using Minimum Relative Entropy Method." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612574/index.pdf.
Повний текст джерелаАнотація:
The interpretation of heart's electrical activity is very important in clinical medicine since contraction of cardiac muscles is initiated by the electrical activity of the heart. The electrocardiogram (ECG) is a diagnostic tool that measures and records the electrical activity of the heart. The conventional 12 lead ECG is a clinical tool that provides information about the heart status. However, it has limited information about functionality of heart due to limited number of recordings. A better alternative approach for understanding cardiac electrical activity is the incorporation of body surface potential measurements with torso geometry and the estimation of the equivalent cardiac sources. The problem of the estimating the cardiac sources from the torso potentials and the body geometry is called the inverse problem of electrocardiography. The aim of this thesis is reconstructing accurate high resolution maps of epicardial potential representing the electrical activity of the heart from the body surface measurements. However, accurate estimation of the epicardial potentials is not an easy problem due to ill-posed nature of the inverse problem. In this thesis, the linear inverse ECG problem is solved using different optimization techniques such as Conic Quadratic Programming, multiple constrained convex optimization, Linearly Constrained Tikhonov Regularization and Minimum Relative Entropy (MRE) method. The prior information used in MRE method is the lower and upper bounds of epicardial potentials and a prior expected value of epicardial potentials. The results are compared with Tikhonov Regularization and with the true potentials.
40
Gzara, Fatma. "Large scale integer programming : a novel solution method and application." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=84254.
Повний текст джерелаАнотація:
Integer programming is a powerful modeling tool for a variety of decision making problems such as in telecommunications network design and in routing and scheduling. Integer programming models of realistic problems are large in size and pose serious challenge to available software. This creates an urgent need for solution methodologies that can deal with their size and complexity. In this thesis, we focus on the theoretical development, implementation and testing of a novel methodology: an interior-point branch-and-price algorithm with cut generation for large scale integer programming.The methodology applies to any integer program but is built for a general class of integer programming that has a large, possibly exponential set of constraints. It starts by applying a decomposition method to the complicating constraints. We focus on Lagrangian relaxation or Dantzig-Wolfe decomposition; both lead to a master problem with an exponential number of variables and constraints. The same analysis applies when one starts by relaxing the exponential constraints and then applying a decomposition method. In both cases, one has to solve iteratively a master problem that is updated by appending violated cuts and columns. For that, we propose a cut and column generation algorithm based on analytic centers.
The cut and column generation algorithm solves a restricted master problem using a primal analytic center cutting plane method to obtain a bound on the original problem. The bound may be poor in quality since most of the complicating constraints are relaxed. To strengthen the bound, we generate violated constraints and append them to the master problem. At this point we use available information to warm-start the solution of the updated restricted master problem. This is done using a dual Newton method to calculate the next analytic center, after which we proceed with the primal method.
The bound is then embedded within a branch-and-bound algorithm leading to a branch-and-price algorithm. In fact, the algorithm is more than a branchand-price since it is able to deal with valid cuts added at the level of the master problem. This is a major step towards an interior-point branch-andcut-and-price algorithm. For an efficient integration of the cut and column generation algorithm within branch-and-bound, we use available information from a parent node to warm-start the calculation of the bound at child nodes. This is achieved by a dual Newton method.
41
Kirkup, Stephen Martin. "Solution of exterior acoustic problems by the boundary element method." Thesis, University of Brighton, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327859.
Повний текст джерела
42
Vasanthakumar, Parthasarathy. "Three dimensional frequency-domain solution method for unsteady turbomachinery flows." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/3089/.
Повний текст джерелаАнотація:
The three-dimensional calculation of unsteady flows is increasingly gaining importance in the prediction of turbomachinery flow problems. A three-dimensional Euler/Navier-Stokes solver incorporating the time-linearized method and the nonlinear harmonic method in the frequency domain has been developed for predicting unsteady turbomachinery flows. In the time-linearized method, the flow is decomposed into a steady part and a harmonic perturbation part. Linearization results in a steady flow equation and a time-linearized perturbation equation. A pseudo-time time-marching technique is introduced to time-march them. A cell centred finite volume scheme is employed for spatial discretization and the time integration involves a four stage Runge Kutta scheme. Nonreflecting boundary conditions are applied for far field boundaries and a slip wall boundary condition is used for Navier-Stokes calculations. In the nonlinear harmonic method, the flow is assumed to be composed of a time-averaged part and an unsteady perturbation part. Due to the nonlinearity of the unsteady equations, time-averaging produces extra unsteady stress terms in the time-averaged equation which are evaluated from unsteady perturbations. While the unsteady perturbations are obtained from solving the harmonic perturbation equation, the coefficients of perturbation equations come from the solution of time-averaged equation and this interaction is achieved through a strong coupling procedure. In order to handle flows with strong nonlinearity, a cross coupling of higher order harmonics through a harmonic balancing technique is also employed. The numerical solution method is similar to that used in the time-linearized method. The numerical validation includes several test cases involving linear and nonlinear unsteady flows with specific attention to flows around oscillating blades. The results have been compared with other well developed linear methods, nonlinear time-marching method and experimental data. The nonlinear harmonic method is able to predict strong nonlinearities associated with shock oscillations well but some limitations have also been observed. A three-dimensional prediction of unsteady viscous flows through a linear compressor cascade with 3D blade oscillation, probably the first of its kind, has shown that unsteady flow calculation in the frequency domain is able to predict three-dimensional blade oscillations reasonably well.
43
Abd, El Aziz Osama Mostafa. "Solution of time dependent problems using the Global Element Method." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329416.
Повний текст джерела
44
Liu, K. M. "Numerical solution of differential Eigenvalue problems with the Tau method." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37766.
Повний текст джерела
45
Chaudhary, Anil Bhaskar. "A solution method for two- and three-dimensional contact problems." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/15272.
Повний текст джерелаАнотація:
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.
Includes bibliographical references.
by Anil Bhaskar Chaudary.
Sc.D.
46
Chi, Ya-Ting, and 紀雅婷. "The method of fundamental solution for Laplace''s equation in 3D." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/k647w2.
Повний текст джерелаАнотація:
碩士國立中山大學
應用數學系研究所
97
For the method of fundamental solutions(MFS), many reports deal with 2D problems. Since the MFS is more advantageous for 3D problems, this thesis is devoted to Laplace''s equation in 3D problems. Since the fundamental solutions(FS) Φ(x,y)=1/(4π||x-y||), x,y∈R^3 are known, the location of source points is important in real computation. In this thesis, we choose a cylinder as the solution domain, and the source points on larger cylinders and spheres. Numerical results are reported, to draw some useful conclusions. The theoretical analysis will be explored in the future.
47
Zhang, Zewei. "Transient bioheat transfer analysis in biological tissues by fundamental-solution-based numerical methods." Phd thesis, 2015. http://hdl.handle.net/1885/15827.
Повний текст джерелаАнотація:
Taylor's expansion approach was applied to linearize the nonlinear term in the original nonlinear bioheat transfer governing equation. Then the DRM and the MFS was established to obtain the particular and homogeneous solutions. The influence of blood perfusion rate on temperature distribution in the skin tissue was analysed by changing the coefficients in the three expressions of blood perfusion rate. Numerical results showed that the variation of blood perfusion rate plays a significant role in the temperature distribution within the skin tissue.
Finally, a meshless numerical scheme combining the operator splitting method (OSM), the RBF interpolation and the MFS was developed for solving transient nonlinear bioheat problems in two-dimensional skin tissue. In the numerical scheme, the nonlinearity caused by the temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the procedure, the OSM is used to separate the Laplacian operator and the nonlinear source term, and then second-order time-stepping schemes are employed for approximating two splitting operators in order to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. The full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations to determine unknowns at each time step. The proposed method was verified by comparison with other methods. Furthermore, the sensitivity of the coefficients in cases of a linear and an exponential relationship of TDBPR was investigated to reveal their bioheat effect on the skin tissue.
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Lo, Lin-Feng, and 羅琳峰. "The Method of Fundamental Solutions for 2D Helmholtz Equation." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/v694hb.
Повний текст джерелаАнотація:
碩士國立中山大學
應用數學系研究所
96
In the thesis, the error and stability analysis is made for the 2D Helmholtz equation by the method of fundamental solutions (MFS) using both Bessel and Neumann functions. The bounds of errors in bounded simply-connected domains are derived, while the bounds of condition number are derived only for disk domains. The MFS using Bessel functions is more efficient than the MFS using Neumann functions. Interestingly, for the MFS using Bessel functions, the radius R of the source points is not necessarily larger than the maximal radius r_max of the solution domain. This is against the traditional condition: r_max < R for MFS. Numerical experiments are carried out to support the analysis and conclusions made.
49
Ting-chun, Daniel, and 吳鼎鈞. "The Trefftz Method using Fundamental Solutions for Biharmonic Equations." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/bcu993.
Повний текст джерелаАнотація:
碩士國立中山大學
應用數學系研究所
96
In this thesis, the analysis of the method of fundamental solution(MFS) is expanded for biharmonic equations. The bounds of errors are derived for the traditional and the Almansi''s approaches in bounded simply-connected domains. The exponential and the polynomial convergence rates are obtained from highly and finite smooth solutions, respectively. Also the bounds of condition number are derived for the disk domains, to show the exponential growth rates. The analysis in this thesis is the first time to provide the rigor analysis of the CTM for biharmonic equations, and the intrinsic nature of accuracy and stability is similar to that of Laplace''s equation. Numerical experiment are carried out for both smooth and singularity problems. The numerical results coincide with the theoretical analysis made. When the particular solutions satisfying the biharmonic equation can be found, the method of particular solutions(MPS) is always superior to MFS, supported by numerical examples. However, if such singular particular solutions near the singular points can not be found, the local refinement of collocation nodes and the greedy adaptive techniques can be used. It seems that the greedy adaptive techniques may provide a better solution for singularity problems. Beside, the numerical solutions by Almansi''s approaches are slightly better in accuracy and stability than those by the traditional FS. Hence, the MFS with Almansi''s approaches is recommended, due to the simple analysis, which can be obtained directly from the analysis of MFS for Laplace''s equation.
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Lee, Cheuk Yu. "Fundamental solution based numerical methods for three dimensional problems: efficient treatments of inhomogeneous terms and hypersingular integrals." Phd thesis, 2016. http://hdl.handle.net/1885/117204.
Повний текст джерелаАнотація:
In recent years, fundamental solution based numerical methods
including the meshless method of fundamental solutions (MFS), the
boundary element method (BEM) and the hybrid fundamental solution
based finite element method (HFS-FEM) have become popular for
solving complex engineering problems. The application of such
fundamental solutions is capable of reducing computation
requirements by simplifying the domain integral to the boundary
integral for the homogeneous partial differential equations. The
resulting weak formulations, which are of lower dimensions, are
often more computationally competitive than conventional
domain-type numerical methods such as the finite element method
(FEM) and the finite difference method (FDM).
In the case of inhomogeneous partial differential equations
arising from transient problems or problems involving body
forces, the domain integral related to the inhomogeneous
solutions term will need to be integrated over the interior
domain, which risks losing the competitive edge over the FEM or
FDM. To overcome this, a particular treatment to the
inhomogeneous term is needed in the solution procedure so that
the integral equation can be defined for the boundary. In
practice, particular solutions in approximated form are usually
applied rather than the closed form solutions, due to their
robustness and readiness. Moreover, special numerical treatment
may be required when evaluating stress directly on the domain
surface which may give rise to hypersingular integral
formulation. This thesis will discuss how the MFS and the BEM can
be applied to the three-dimensional elastic problems subjected to
body forces by introducing the compactly supported radial basis
functions in addition to the efficient treatment of hypersingular
surface integrals. The present meshless approach with the MFS and
the compactly supported radial basis functions is later extended
to solve transient and coupled problems for three-dimensional
porous media simulation.