Orientadores: Anamaria Gomide, Jorge Stolfi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-13T10:58:35Z (GMT). No. of bitstreams: 1 Pereira_DanilloRoberto_M.pdf: 891270 bytes, checksum: 71a9debc6a10f8de7083dd3e33c649a6 (MD5) Previous issue date: 2009 / Resumo: A geração de imagens fotorrealisticas e um desafio importante em computação gráfica. Um ingrediente critico para a obtenção do realismo esta o modelo de iluminação. Em 1986, Jim Kajiya apresentou uma equação integral que define o fluxo de luz (radiosidade) num ambiente de maneira precisa; contudo, ate recentemente, os métodos conhecidos para a resolução dessa equação tinham custo computacional e complexidade de implementação elevados. Em 2008, Jaako Lehtinen desenvolveu uma técnica relativamente simples e eficiente para o calculo da iluminação global em cenas virtuais, usando elementos finitos definidos por pontos de amostragem. Neste projeto de Mestrado, implementamos esse método, e comparamos o resultado usando três tipos diferentes de bases: uma base radial, uma base radial normalizada e uma base de Shepard. Alem da comparação visual, calculamos a radiosidade "exata" para uma cena simples e comparamos quantitativamente esse resultado com os resultados do método de Lehtinen com cada uma das três bases. / Abstract: The generation of realistic images is a major challenge in computer graphics. A critical ingredient for realistic rendering is the lighting model. In 1986, Jim Kajiya presented an integral equation that precisely defines the light flow (radiosity) in a virtual environment; however, until recently, the known methods for solving that equation had high computational cost and implementation complexity. In 2008, Jaako Lehtinen developed a relatively simple and efficient technique for the computation of global illumination in virtual scenes, using finite elements defined by sampling points. In this Masters project, we implemented that method, and compared the results using three different types of bases: a radial basis, a normalized radial basis, and a Shepard basis. Besides visual comparison, we computed the "exact" radiosity for a simple scene and compared quantitatively that result with the results obtained by Lehtinen's method with each of the three bases. / Mestrado / Computação Grafica / Mestre em Ciência da Computação

In this thesis, the method of Proper Orthogonal Decomposition (POD) is implemented to construct approximate, reduced order models (ROM) of mesh movement methods. Three mesh movement algorithms are implemented and comparatively evaluated, namely radial basis function interpolation, mesh optimization and elastic deformation. POD models of the mesh movement algorithms are constructed using a series of system observations, or snapshots of a given mesh for a set of boundary deformations. The scalar expansion coefficients for the POD basis modes are computed in three different ways, through coefficient optimization, Galerkin projection of the governing set of equations and coefficient interpolation. It is found that using only coefficient interpolation yields mesh movement models that accurately approximates the full order mesh movement, with CPU cost savings in excess of 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

Microsized hexagonal gallium nitride pyramids show promise as next generation Light Emitting Diodes (LEDs) due to certain quantum properties within the pyramids. One metric for evaluating the efficiency of a LED device is by studying its Light Extraction Efficiency (LEE). To calculate the LEE for different pyramid designs, simulations can be performed using the FDTD method. Maximizing the LEE is treated as a black-box optimization problem with an interpolation method that utilizes radial basis functions. A simple heuristic is implemented and tested for various pyramid parameters. The LEE is shown to be highly dependent on the pyramid size, the source position and the polarization. Under certain circumstances, a LEE over 17% is found above the pyramid. The results are however in some situations very sensitive to the simulation parameters, leading to results not converging properly. Establishing convergence for all simulation evaluations must be done with further care. The results imply a high LEE for the pyramids is possible, which motivates the need for further research.

In this paper the obstacle description with Radial Basis Functions for contact problems in three dimensional elasticity will be done. A short Introduction of the idea of Radial Basis Functions will be followed by the usage of Radial Basis Functions for approximation of isosurfaces. Then these isosurfaces are used for the obstacle-description in three dimensional elasticity contact problems. In the last part some computational examples will be shown.

Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.

Karst rocky desertification is a progressive process of land degradation in karst regions in which soil is severely, or completely, eroded. This process may be caused by natural factors, such as geological structure, and population pressure leading to poor ecosystem health and lagging economic development. Karst rocky desertification is therefore a significant obstacle to sustainable development in southwest China. We applied a radial basis function network model to assess the risk of karst rocky desertification in northwest Guangxi, a typical karst region located in southwest China. Factors known to influence karst rocky desertification were evaluated using remote sensing and geographic information systems techniques to classify the 23 counties in the study area from low to extreme risk of karst rocky desertification. Counties with extreme or strong karst rocky desertification risk (43.48%, nearly half of the study area) were clustered in the north, central and southeast portions of the study area. Counties with low karst rocky desertification (30.43%) were located in the west, northeast and southwest of the study area. The spatial distribution of karst rocky desertification was moderately correlated to population density.

The Growth Curve Model is a bilinear statistical model which can be used to analyse several groups of repeated measurements. Normally the Growth Curve Model is defined in such a way that the permitted sampling frequency of the repeated measurement is limited by the number of observed individuals in the data set.In this thesis, we examine the possibilities of utilizing highly frequently sampled measurements to increase classification accuracy for real world data. That is, we look at the case where the regular Growth Curve Model is not defined due to the relationship between the sampling frequency and the number of observed individuals. When working with this high frequency data, we develop a new method of basis selection for the regression analysis which yields what we call a Bilinear Gaussian Radial Basis Function Network (BGRBFN), which we then compare to more conventional polynomial and trigonometrical functional bases. Finally, we examine if Tikhonov regularization can be used to further increase the classification accuracy in the high frequency data case.Our findings suggest that the BGRBFN performs better than the conventional methods in both classification accuracy and functional approximability. The results also suggest that both high frequency data and furthermore Tikhonov regularization can be used to increase classification accuracy.

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When modeling interest rates, using strong formulations of underlying differential equations is prone to bad numerical approximations and high computational costs, due to close to non-smoothness in the probability density function of the interest rate. To circumvent these problems, a weak formulation of the Fokker–Planck equation using Gaussian radial basis functions is suggested. This approach is used in a parameter estimation process for two interest rate models: the Vasicek model and the Cox–Ingersoll–Ross model. In this thesis, such an approach is shown to yield good numerical approximations at low computational costs.

This thesis explores the application of Radial Basis Functions (RBFs) to fluid dynamical problems. In particular, stationary Stokes and Navier-Stokes equations are solved using RBF collocation method. An existing approach from the literature, is enchanced by an additional polynomial basis and a new preconditioner. A faster method based on the partition of unity is introduced for stationary Stokes equations. Finally, a global method based on Picard linearization is introduced for stationary Navier-Stokes equations. / Denna avhandling utforskar tillämpningen av Radial Basis Functions (RBF) på dynamiska problem med vätskor. I synnerhet löses stationära Stokes och Navier-Stokes ekvationer lösas med hjälp av RBF-samlokaliseringsmetoden. En befintlig metod från litteraturen, förbättras genom en ytterligare polynombas och en ny förkonditionering. En snabbare metod baserad på enhetens partition introduceras för stationära Stokes-ekvationer. Slutligen introduceras en global metod baserad på Picard linjärisering för stationära Navier-Stokes ekvationer.