In order to determine the validity and the quality of meshes, mesh optimization methods have been formulated with quality measures. The basic idea of mesh optimization is to relocate the vertices to obtain a valid mesh (untangling) or improve the mesh quality (smoothing), or both. We will look at a new algebraic way of calculating quality measure on quadrilateral meshes, based on triangular meshes in 2D as well as new optimization methods for simultaneous untangling and smoothing for severely deformed meshes. An innovative anisotropic diffusion method will be introduced for consideration of inner boundary deformation movements for quadrangle meshes in 2D.

O objetivo deste trabalho é o desenvolvimento de \"software\" para proteção digital das linhas de transmissão. Com esse propósito são implementados relés de distância com características quadrilaterais e adaptativas. Um \"software\" básico para este fim consiste de várias etapas como: detecção da falta, filtragem digital, classificação da falta, cálculo da impedância aparente e verificação das zonas de proteção. Na etapa de filtragem digital das ondas, é utilizada a Transformada Discreta de Fourier (TDF) para a extração dos componentes fundamentais de tensão e corrente. A característica quadrilateral mostra-se eficiente para determinadas condições de operação fixas do sistema, mas seu desempenho é comprometido quando ocorrem mudanças das mesmas. Para solucionar este problema, é introduzida a teoria de relés adaptativos onde a característica de abertura do relé digital muda com as alterações nas condições de operação do sistema, mantendo-se assim a eficiência da proteção. / The objective of this work is the development of a software for digital protection of transmission lines. For this purpose relays of distance with Quadrilateral and Adaptive characteristics are implemented. A basic software with this aim consists of several steps such as: detection of the fault, digital filtering of the faulted waves, classification of the fault, impedance calculation and verification of the protection zones. For the digital filtering purpose, the Fourier Discret Transform, is used in order to extract the fundamental phasors of voltages and currents. Quadrilateral characteristcs are shown to be effective under certain operation conditions of the system, but its performance is not so efficient when those conditions are changed. In order to solve these problems, the theory of adaptive relays was introduced whereby the characteristic of digital relay changes according to the alterations in the conditions of the system operation, and by these means the protection is kept efficient.

O objetivo deste trabalho é o desenvolvimento de \"software\" para proteção digital das linhas de transmissão. Com esse propósito são implementados relés de distância com características quadrilaterais e adaptativas. Um \"software\" básico para este fim consiste de várias etapas como: detecção da falta, filtragem digital, classificação da falta, cálculo da impedância aparente e verificação das zonas de proteção. Na etapa de filtragem digital das ondas, é utilizada a Transformada Discreta de Fourier (TDF) para a extração dos componentes fundamentais de tensão e corrente. A característica quadrilateral mostra-se eficiente para determinadas condições de operação fixas do sistema, mas seu desempenho é comprometido quando ocorrem mudanças das mesmas. Para solucionar este problema, é introduzida a teoria de relés adaptativos onde a característica de abertura do relé digital muda com as alterações nas condições de operação do sistema, mantendo-se assim a eficiência da proteção. / The objective of this work is the development of a software for digital protection of transmission lines. For this purpose relays of distance with Quadrilateral and Adaptive characteristics are implemented. A basic software with this aim consists of several steps such as: detection of the fault, digital filtering of the faulted waves, classification of the fault, impedance calculation and verification of the protection zones. For the digital filtering purpose, the Fourier Discret Transform, is used in order to extract the fundamental phasors of voltages and currents. Quadrilateral characteristcs are shown to be effective under certain operation conditions of the system, but its performance is not so efficient when those conditions are changed. In order to solve these problems, the theory of adaptive relays was introduced whereby the characteristic of digital relay changes according to the alterations in the conditions of the system operation, and by these means the protection is kept efficient.

This dissertation examines the evangelicalism of Alexander Carson (ca. 1776- 1844) using David Bebbington's evangelical quadrilateral--biblicism, crucicentrism, conversionism, and activism--as a framework. Chapter 1 gives an introduction to the study and a biographical sketch of Carson's life and ministry. Chapter 2 examines Carson's view of Scripture in the areas of inspiration, Bible translation, and the transmission of Scripture. Carson's views on the inspiration of Scripture and the principles by which it was to be translated were given within the context of the theological controversies in which he was involved. Chapter 3 examines Carson's view of the atonement. It looks at his understanding of humanity's sin, divine justice and mercy, God's sovereignty, and the completed nature of the atonement. Chapter 4 is a study of Carson's understanding of how people are converted. The chapter discusses his views on the definition of saving faith, the relation between faith and works, the conversion experience, and the divine role in conversion. Chapter 5 looks at Carson's views on evangelism in four areas: the use of the Bible in evangelism, the importance of religious liberty to evangelize, the role of divine providence in evangelism, and the Christian's duty to evangelize. Although the four characteristics of evangelicalism set forth by Bebbington do not include other areas of theology important to Carson, such as his views on baptism and church order, the quadrilaterial does focus on what Carson believed to be central to Christianity, namely, the gospel. Therefore, considering Bebbington's quadrilateral to be a sound framework for understanding Carson's view of the gospel, the thesis of this study is that Carson's belief in the Bible as a verbally and completely inspired text was an infallible source for his understanding of the gospel as being centered upon the atonement, effective through justification by faith alone, and the motivation for evangelism. / This dissertation was under embargo until 2014-05-23.

[pt] Um dos principais desafios para a geração de malhas de quadriláteros é garantir o alinhamento dos elementos em relação às restrições do domínio. Malhas não alinhadas introduzem problemas numéricos em simulações que usam essas malhas como subdivisão do domínio. No entanto, não existe uma métrica de alinhamento para a avaliação de qualidade de malhas de quadriláteros. Um campo de direcionalidade representa a difusão das orientações das restrições no interior do domínio. Kowalski et al. usam um campo de direcionalidade para particionar o domínio em regiões quadrilaterais. Neste trabalho, reproduzimos o método de particionamento proposto por Kowalski et al. com algumas alterações, visando reduzir o número final de partições. Em seguida, propomos uma métrica para avaliar a qualidade de malhas de quadriláteros em relação ao alinhamento com as restrições do domínio. / [en] One of the main challenges in quadrilateral mesh generation is to ensure the alignment of the elements with respect to domain constraints. Unaligned meshes insert numerical problems in simulations that use these meshes as a domain discretization. However, there is no alignment metric for evaluating the quality of quadrilateral meshes. A directionality field represents the diffusion of the constraints orientation to the interior of the domain. Kowalski et al. use a directionality field for domain partitioning into quadrilateral regions. In this work, we reproduce their partitioning method with some modifications, aiming to reduce the final number of partitions. We also propose a metric to evaluate the quality of a quadrilateral mesh with respect to the alignment with domain constraints.

The purpose of this thesis is to develop web-based modules for enhancing instruction of the geometry sections of the Virginia Standards of Learning in the seventh and eighth grades. While all of Virginia's seventh and eighth grade Standards of Learning strands are certainly worthy of these types of modules, geometry appeals to me most because of the vast amount of web-based resources that will be valuable when organized into modules. It is my hope that teachers of these grades will find this useful in their instruction of geometry.

In most finite element analysis, a uniform mesh is not the optimum way to model the problem. Mesh adaptation is the ability to modify a finite element model to include regions of the mesh with higher and lower node density. Mesh adaptation has received extensive study in both computational mechanics and computer graphics to increase the resolution or accuracy of the solution in specific areas. The algorithm developed in this thesis, the Automated Quadrilateral Coarsening by Ring Collapse (AQCRC) algorithm, provides a unique solution to allow conformal coarsening of both structured and unstructured quadrilateral finite element meshes. The algorithm is based on dual chord operations and dual chord removal. The AQCRC algorithm follows six steps: 1) input of a coarsening region and factor, 2) selection of coarsening rings, 3) improvement of mesh quality, 4) removal of coarsening rings, 5) mesh clean-up and 6) coarsening iterations. Examples are presented that show the application of the algorithm.

This thesis presents a new approach to conformal all-quadrilateral mesh adaptation. In finite element modeling applications, it is often desirable to modify the node density of the mesh; increasing the density in some parts of the mesh to provide more accurate results, while decreasing the density in other parts to reduce computation time. The desired node density is typically determined by a sizing function based on either the geometry of the model or the results of a finite element solution. Although there are numerous mesh adaptation methods currently in use, including initial adaptive mesh generation, node redistribution, and adaptive mesh refinement, there are relatively few methods that modify the mesh density by adding and removing mesh elements, and none of these guarantee a conformal, all-quadrilateral mesh while allowing general coarsening. This work introduces a new method that incorporates both conformal refinement and coarsening strategies on an existing mesh of any density or configuration. Given a sizing function, this method modifies the mesh by combining existing template based quadrilateral refinement methods with recent developments in localized quadrilateral coarsening and quality improvement into an automated mesh adaptation routine.

The ability to effectively adapt a mesh is a very important feature of high fidelity finite element modeling. In a finite element analysis, a relatively high node density is desired in areas of the model where there are high error estimates from an initial analysis. Providing a higher node density in such areas improves the accuracy of the model and reduces the computational time compared to having a high node density over the entire model. Node densities can be determined for any model using the sizing functions based on the geometry of the model or the error estimates from the finite element analysis. Robust methods for mesh adaptation using sizing functions are available for refining triangular, tetrahedral, and quadrilateral elements. However, little work has been published for adaptively refining all hexahedral meshes using sizing functions. This thesis describes a new approach to drive hexahedral refinement based upon an error sizing function and a mechanism to compare the sizes of the node after refinement.

The effective generation high quality quadrilateral surface meshes is an area of important research and development for the finite element community. Quadrilateral elements generally lead to more efficient and accurate finite results. In addition, some all hexahedral volume meshing algorithms are based on an initial quadrilateral mesh surface mesh that has specific connectivity requirements. This thesis presents a new and unique procedure named "Surfaced Splicing". Surface Splicing allows for the generation of all quadrilateral surface meshes as well as the ability to edit these meshes via the dual. The dual contains the same data as the mesh but, unlike the mesh, the dual directly allows the visualization of how surface and volume elements interrelate and connect with one another. The dual also provides mesh connectivity information that is crucial in forming an all-quadrilateral surface mesh that can form the basis of an all-hexahedral volume mesh.