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Novel stable subgridding algorithm in finite difference time domain methodKrishnaiah, K. Mohana January 1997 (has links)
No description available.
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Study on tribology analysis of chemical mechanical polishingChen, Chin-cheng 27 August 2007 (has links)
During the CMP process, a wafer is rotated and pressed face down against a rotating polishing pad. Polishing slurry is delivered on the top of pad continuously and forms a thin lubricating film between the wafer and the pad. In this study, a three-dimensional slurry flow model based on a generalized Reynolds equation is developed, which can apply to a rough pad with the compressibility of the pad, and the multi-grid method is used to reduce computational time. According to the force and moment balance equations, the tilted angles and the slurry film thickness can be evaluated. When the pad surface is rough, the squeeze term differentiated by time should be considered in this model due to the rotation of the pad. The influences of applied load, pad speed, wafer speed, pad compressibility, and surface roughness pattern on the tilted angles and the slurry film thickness are investigated. Results show that the variation of the tilted angles becomes more significant for the anisotropic than that for the isotropic during the rotation of the pad. And the slurry film thickness at the center of the wafer increases as applied load decreases or pad speed increases or wafer speed decreases or the compressibility of the pad increases.
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Algoritmo genético acoplado a um método multi-grid e a teoria dos grafos para determinação da estrutura de equilíbrio de aglomerados atômicos / Genetic algorithm coupled to a multi-grid method and the graph teory to the determination of the equilibrium structure of atomic clustersBaldez, Raisi Natalia Lenz 14 December 2012 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we present a proposal to improve Genetic Algorithm method by coupling
it to the techniques of discretization of the configurational space via the multi-grid
methodology, and by employing a topological selection of the offsprings via graph theory.
The best performance for clusters of 13 and 19 aluminum atoms shows that the multi-grid
tecniques can increase the efficiency of the genetic algorithm, mainly when a more extensive
search is performed in an initially sparse grid of points. We also show that a greater
improvement in the efficiency of the genetic algorithm can be obtained when we select
the offsprings of the sucessive generations in order to be topologically distinct from each
other. / Neste trabalho apresentamos uma proposta de melhoria do método do Algoritmo
Genético (AG) em que se acopla a este método as técnicas de discretização do espaço
configuracional via métodos de multi-grid e emprega-se uma seleção topológica dos indivíduos
que compõem a população via métodos extraídos da teoria dos grafos. Testes
realizados para os aglomerados de alumínio de 13 e 19 átomos mostram que as técnicas
de multi-grid podem aumentar a eficiência do AG, principalmente quando emprega-se esquemas
de discretização em que se realiza uma busca mais refinada nos estágios iniciais
do processo de busca, em que a malha (grid) de pontos no espaço configuracional é
mais esparso. Nosso estudo também mostrou que um ganho ainda mais significativo de
eficiência do AG é obtido quando selecionamos as configurações das seguidas gerações
de indivíduos, de modo a que sejam topologicamente distintas uma das outras.
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Multi-level solver for degenerated problems with applications to p-versions of the femBeuchler, Sven 18 July 2003 (has links) (PDF)
Dissertation ueber die effektive Vorkonditionierung linearer Gleichungssysteme
resultierend aus der Diskretisierung eines elliptischen Randwertproblems 2. Ordnung mittels
der Methode der Finiten Elementen.
Als Vorkonditionierer werden multi-level artige Vorkonditionierer (BPX, Multi-grid, Wavelets) benutzt.
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A Multi-Grid Method for Generalized Lyapunov EquationsPenzl, Thilo 07 September 2005 (has links) (PDF)
We present a multi-grid method for a class of
structured generalized Lyapunov matrix equations.
Such equations need to be solved in each step of
the Newton method for algebraic Riccati equations,
which arise from linear-quadratic optimal control
problems governed by partial differential equations.
We prove the rate of convergence of the two-grid
method to be bounded independent of the dimension
of the problem under certain assumptions.
The multi-grid method is based on matrix-matrix
multiplications and thus it offers a great
potential for a parallelization. The efficiency
of the method is demonstrated by numerical
experiments.
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Rotations in 2D and 3D discrete spacesThibault, Yohan 22 September 2010 (has links) (PDF)
This thesis presents a study on rotation in 2 dimensional and 3 dimensional discrete spaces. In computer science, using floating numbers is problematic due to computation errors. Thus we chose during this thesis to work only in discrete space. In the field of computer vision, the rotation is a transformation required for many applications. Using discretized Euclidean rotation gives bad results. Then, it is necessary to develop new rotation methods adapted to the discrete spaces. We mainly studied the hinge angles that represent the discontinuity of the rotation in the discrete space. Indeed, it is possible to perform two rotations of the same digital image with two angles that are slightly different and obtain the same result. This is captured by hinge angles. Using these angles allow us to describe a discrete rotation that gives the same results than the discretized Euclidean rotation without using floating numbers. They also allow describing an incremental rotation that performs all possible rotations of a given digital image. Using hinge angles can also be extended to the rotations in 3 dimensional discrete spaces. The extension requires the multi-grids that are rotation planes containing three sets of parallel lines. These parallel lines represent the discontinuities of the rotation in 3D discrete space. Thus they are useful to describe the hinge angles in rotation planes. Multi-grids allow obtaining the same results in 3D discrete rotations than the results obtained in 2D discrete rotations. This thesis presents a study on rotation in 2 dimensional and 3 dimensional discrete spaces. In computer science, using floating numbers is problematic due to computation errors. Thus we chose during this thesis to work only in discrete space. In the field of computer vision, the rotation is a transformation required for many applications. Using discretized Euclidean rotation gives bad results. Then, it is necessary to develop new rotation methods adapted to the discrete spaces. We mainly studied the hinge angles that represent the discontinuity of the rotation in the discrete space. Indeed, it is possible to perform two rotations of the same digital image with two angles that are slightly different and obtain the same result. This is captured by hinge angles. Using these angles allow us to describe a discrete rotation that gives the same results than the discretized Euclidean rotation without using floating numbers. They also allow describing an incremental rotation that performs all possible rotations of a given digital image. Using hinge angles can also be extended to the rotations in 3 dimensional discrete spaces. The extension requires the multi-grids that are rotation planes containing three sets of parallel lines. These parallel lines represent the discontinuities of the rotation in 3D discrete space. Thus they are useful to describe the hinge angles in rotation planes. Multi-grids allow obtaining the same results in 3D discrete rotations than the results obtained in 2D discrete rotations
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Parallelization of multi-grid methods based on domain decomposition ideasJung, M. 30 October 1998 (has links) (PDF)
In the paper, the parallelization of multi-grid methods for solving second-order elliptic boundary value problems in two-dimensional domains is discussed. The parallelization strategy is based on a non-overlapping domain decomposition data structure such that the algorithm is well-suited for an implementation on a parallel machine with MIMD architecture. For getting an algorithm with a good paral- lel performance it is necessary to have as few communication as possible between the processors. In our implementation, communication is only needed within the smoothing procedures and the coarse-grid solver. The interpolation and restriction procedures can be performed without any communication. New variants of smoothers of Gauss-Seidel type having the same communication cost as Jacobi smoothers are presented. For solving the coarse-grid systems iterative methods are proposed that are applied to the corresponding Schur complement system. Three numerical examples, namely a Poisson equation, a magnetic field problem, and a plane linear elasticity problem, demonstrate the efficiency of the parallel multi- grid algorithm.
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Numerical simulations of vortices near free and solid surfacesLuton, J. Alan 05 October 2007 (has links)
The interaction of vortices passing near free and solid surfaces has been examined using direct numerical simulation (DNS). A computer code was developed which solves the unsteady, three-dimensional Navier-Stokes equations for incompressible flow. A critical element of the numerical scheme is the efficient solution of Poisson's equation. A state of the art solver based on multigrid techniques was developed which gives excellent convergence rates. The result is a tool capable of modeling complex three-dimensional flows in a variety of configurations.
Three different flow fields have been examined in order to determine some of the complex interactions involved between a vortex and a surface. The first concerns the two-dimensional interaction between a boundary layer and a convecting vortex. The size and height above the wall of the vortex are the same order of magnitude as the boundary layer thickness. A strong primary vortex creates a secondary vortex which causes the rebound of the primary, a response observed in many previous studies. However, weaker vortices as well do not follow the inviscid trajectory despite the absence of a secondary vortex. Rather than creating vorticity at the wall, a weaker vortex mainly redistributes the vorticity of the boundary layer. The redistributed vorticity alters the path of the vortex in ways not seen for vortex/wall interactions. / Ph. D.
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Rotations in 2D and 3D discrete spaces / Rotations dans les espaces discrets 2D et 3DThibault, Yohan 22 September 2010 (has links)
Cette thèse présente une étude sur les rotations dans les espaces discrets en 2 dimensions et en 3 dimensions. Dans le cadre de l'informatique, l'utilisation des nombres flottants n'est pas recommandée du fait des erreurs de calculs que cela implique. Nous avons donc fait le choix de nous concentrer sur les espaces discrets. Dans le domaine de la vision par ordinateur, la rotation est une transformation requise pour de nombreuses applications. L'utilisation de la rotation continue discrétisée donne des résultats de mauvaise qualité. Pour cette raison, il est nécessaire de développer de nouvelles méthodes de rotation adaptées aux espaces discrets. Nous nous sommes principalement intéressés aux angles charnières qui représentent la discontinuité de la rotation dans les espaces discrets. Dans ces espaces, deux rotations d'une image avec deux angles très proches peuvent donner le même résultat, ce qui est capturé par les angles charnières. L'utilisation de ces angles permet de décrire une rotation qui donne les mêmes résultats que la rotation continue discrétisée tout en n'utilisant que des nombres entiers. Ils permettent aussi de définir une rotation incrémentale qui décrit toutes les rotations possibles d'une image digitale donnée. Les angles charnières peuvent être étendus dans les espaces discrets en trois dimensions. Pour cela, on définit les multi-grilles qui sont des plans de rotations contenant trois ensembles de droites parallèles. Elles représentent les discontinuités de la rotation en 3D. Les multi-grilles permettent d'obtenir les mêmes résultats en 3D que ceux obtenus en 2D / This thesis presents a study on rotation in 2 dimensional and 3 dimensional discrete spaces. In computer science, using floating numbers is problematic due to computation errors. Thus we chose during this thesis to work only in discrete space. In the field of computer vision, the rotation is a transformation required for many applications. Using discretized Euclidean rotation gives bad results. Then, it is necessary to develop new rotation methods adapted to the discrete spaces. We mainly studied the hinge angles that represent the discontinuity of the rotation in the discrete space. Indeed, it is possible to perform two rotations of the same digital image with two angles that are slightly different and obtain the same result. This is captured by hinge angles. Using these angles allow us to describe a discrete rotation that gives the same results than the discretized Euclidean rotation without using floating numbers. They also allow describing an incremental rotation that performs all possible rotations of a given digital image. Using hinge angles can also be extended to the rotations in 3 dimensional discrete spaces. The extension requires the multi-grids that are rotation planes containing three sets of parallel lines. These parallel lines represent the discontinuities of the rotation in 3D discrete space. Thus they are useful to describe the hinge angles in rotation planes. Multi-grids allow obtaining the same results in 3D discrete rotations than the results obtained in 2D discrete rotations. This thesis presents a study on rotation in 2 dimensional and 3 dimensional discrete spaces. In computer science, using floating numbers is problematic due to computation errors. Thus we chose during this thesis to work only in discrete space. In the field of computer vision, the rotation is a transformation required for many applications. Using discretized Euclidean rotation gives bad results. Then, it is necessary to develop new rotation methods adapted to the discrete spaces. We mainly studied the hinge angles that represent the discontinuity of the rotation in the discrete space. Indeed, it is possible to perform two rotations of the same digital image with two angles that are slightly different and obtain the same result. This is captured by hinge angles. Using these angles allow us to describe a discrete rotation that gives the same results than the discretized Euclidean rotation without using floating numbers. They also allow describing an incremental rotation that performs all possible rotations of a given digital image. Using hinge angles can also be extended to the rotations in 3 dimensional discrete spaces. The extension requires the multi-grids that are rotation planes containing three sets of parallel lines. These parallel lines represent the discontinuities of the rotation in 3D discrete space. Thus they are useful to describe the hinge angles in rotation planes. Multi-grids allow obtaining the same results in 3D discrete rotations than the results obtained in 2D discrete rotations
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Multi-level solver for degenerated problems with applications to p-versions of the femBeuchler, Sven 11 July 2003 (has links)
Dissertation ueber die effektive Vorkonditionierung linearer Gleichungssysteme
resultierend aus der Diskretisierung eines elliptischen Randwertproblems 2. Ordnung mittels
der Methode der Finiten Elementen.
Als Vorkonditionierer werden multi-level artige Vorkonditionierer (BPX, Multi-grid, Wavelets) benutzt.
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