Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle multiply-connected transition elements and self-intersecting hexahedral sheets. The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle the above stated problems. These two refinement methods are: 1) element by element refinement and 2) directional refinement. In element by element refinement, the three inherent directions of a hexahedron are refined in one step using one of seven templates. Because of its computational superiority over directional refinement, but its inability to handle multiply-connected transition elements, element by element refinement is used in all areas of the specified region except regions local to multiply-connected transition elements. The directional refinement scheme refines the three inherent directions of a hexahedron separately on a hexahedron by hexahedron basis. This differs from sheet refinement which refines hexahedra using hexahedral sheets. Directional refinement is able to correctly handle multiply-connected transition elements. A ranking system and propagation scheme allow directional refinement to work within the confines of the Selective Approach Algorithm.

Finite element mesh adaptation methods can be used to improve the efficiency and accuracy of solutions to computational modeling problems. For many finite element modeling applications, a conforming all-hexahedral mesh is preferred. When adapting a hexahedral mesh, localized modifications that preserve topologic conformity are often desired. Effective hexahedral refinement methods that satisfy these criteria have recently become available. However, due to hexahedral mesh topology constraints, little progress has been made in the area of hexahedral coarsening. This thesis presents a new method to locally coarsen conforming all-hexahedral meshes. The method works on both structured and unstructured meshes and is not based on undoing previous refinement. Building upon recent developments in quadrilateral coarsening, the method utilizes hexahedral sheet and column operations, including pillowing, column collapsing, and sheet extraction. A general algorithm for automated coarsening is presented and examples of models that have been coarsened are shown. While results are promising, further work is needed to improve the automated process.

It is well known that TCP performs poorly in wireless mesh networks. There has been intensive research in this area, but most work uses simulation as the only evaluation method; however, it is not clear whether the performance gains seen with simulation will translate into benefits on real networks. To explore this issue, we have implemented ATP (Ad-hoc Transport Protocol), a transport protocol designed specifically for wireless ad hoc networks. We have chosen ATP because it uses a radically different design from TCP and because reported results claim significant improvement over TCP. We show how ATP must be modified in order to be implemented in existing open-source wireless drivers, and we perform a comprehensive performance evaluation on mesh testbeds under different operating conditions. Our results show that the performance of ATP is highly sensitive to protocol parameters, especially the epoch timeout value. To improve its performance we design an adaptive version that utilizes a self-adjustable feedback mechanism instead of a fixed parameter. A comprehensive measurement study demonstrates the advantages of our adaptive ATP under various operating conditions. For networks with high bit-rate, low quality links, our adaptive version of ATP demonstrates an average of more than 50% gain in goodput over the default ATP for a single flow case. With respect to fairness, the adaptive ATP generally outperforms the default ATP by an order of magnitude in most results.

Internet rate control protocols, such as TCP, encounter severe performance problems in wireless mesh networks. Because wireless networks use shared communication channels, contention and interference can significantly degrade flow throughput and fairness. Existing research takes either an engineering-based or optimization-based approach to solve the performance problems. The engineering-based approach usually solves a specific observed problem, but does not necessarily optimize the overall performance. The optimization-based approach mathematically models the network to find the optimal resource allocation among competing flows. The model can lead to a distributed rate control algorithm with performance guarantees, but relatively little work has been done to verify that the algorithm leads to good performance in real networks. This dissertation develops a more accurate network optimization model, implements the derived distributed rate control algorithm in a mesh testbed, and discusses observations in the extensive experiments. We first synthesize models used for optimizing fair rate control for wireless mesh networks, and discuss their tradeoffs. We then propose a partial interference model which uses more accurate objective functions and constraints as compared to the binary interference model. Numerical results show that the partial interference model outperforms the binary interference model in all scenarios tested, and the results also suggest that partial interference should be modeled separately from contention. Our experimental results confirm the prevalence of partial interference in our mesh testbed, and show that the partial interference model results in significantly improved performance in a typical interference topology. We also observe a significant deviation between theory and practice, whereby, the assumption of a linear relationship between interfering links breaks in our experiments. We discuss several directions to further investigate this issue.

When used in a wireless mesh network, TCP has shortcomings in the areas of throughput and fairness among traffic flows. Several methods have been proposed to deal with TCP's weakness in a wireless mesh, but most have been evaluated with simulations rather than experimentally. We evaluate several major enhancements to TCP – pacing, conservative windows, and delayed ACKs – to determine whether they improve performance or fairness in a mesh network operating in the BYU Computer Science building. We also draw conclusions about the effectiveness of wireless network simulators based on the accuracy of reported simulation results.

The development of algorithms that effectively modify all-hexahedral finite element mesh is currently an active area of research. Mesh modification can be used to improve mesh quality reduce the time required to mesh a model, and improve the finite element analysis results. However, general modification of all-hexahedral meshes has proven difficult because of the global effects of local modifications. This thesis explains the global constraints on modifying all-hexahedral meshes and then presents three mesh modification techniques that make it possible to do local modifications while accounting for the global effects. These techniques are sheet insertion, sheet extraction, and mesh cutting. Sheet insertion is used to refine a mesh by inserting sheets of hexahedral elements into existing meshes. Sheet extraction coarsens existing meshes by deleting sheets of elements from the mesh. Mesh cutting is used to modify a simple mesh to fit it to complex geometric feature. The mesh modification techniques are covered in detail with representative graphics. Examples are given that demonstrate the application of each technique to the mesh generation process.

This thesis presents the development and evaluation of the knife finite element which is a degenerate case of a hexahedral element. The knife connectivity is an artifact of automatic all-hexahedral mesh generators. Currently, knives are propagated to the surface of the mesh for removal. However since this disturbs the surface mesh, other alternatives are needed. This thesis investigates the option of leaving the knife connectivity in the mesh and treating it as a valid finite element. The shape functions and stiffness matrix for the knife element are derived and evaluated using theoretical and practical evaluations. It is concluded that the knife finite element is a viable element and should be used in finite element analysis when the knife connectivity occurs. Using the knife element reduces the work involved with fixing the knife connectivity by propagation or other means and will produce acceptable results in most cases.

[pt] Este trabalho apresenta um algoritmo de construção de malhas em grafos conexos orientados definidos pela matriz de incidência. Se o grafo é planar e conexo é obtida a matriz de malhas, com o fim de permitir alternativa de análises, por nós ou malhas, de redes elétricas lineares ativas descritas apenas por seus nós. Foi desenvolvido também um algoritmo que realiza essas 2 análises e que aceita elementos ideais como fontes de tensão e corrente, controladas ou não, amplificadores operacionais ideais, indutâncias mútuas. A dimensão do programa foi reduzida pelo fato da representação de um elementos em um método ser igual a de seu dual em outro método. É feita também uma comparação entre os métodos de anos métodos de análise existente. / [en] An algorithm is presented that defines all the internal meshes of na oriented connected graph described by its incidence matrix. In the case of a planar, connected graph, a mesh matrix is obtained, which allows either nodal or mesh analysis of an active linear network described by its nodes. A further algorithm is developed ehich applies both these types of analysis to networks with ideal elements, such as controlled or uncontrolled current and voltage sources, operational amplifiers and mutual inductances. Owing to the fact that the representation of an element in one of these methods is identical to that of the dual element in the other, a program which performs nodal analysis may easily be adapted to perform mesh analysis. The methods are compared with existing methods of circuit analysis and some conclusions are drawn.

A method for extracting linear raised features from laser scanned altimetry (LiDAR) datasets is presented. The objective is to automate the method so that elements in a coastal storm surge simulation finite element mesh might have their edges aligned along vertical terrain features. Terrain features of interest are those that are high and long enough to form a hydrodynamic impediment while being narrow enough that the features might be straddled and not modeled if element edges are not purposely aligned. These features are commonly raised roadbeds but may occur due to other manmade alterations to the terrain or natural terrain. The implementation uses the TauDEM watershed delineation software included in the MapWindow open source Geographic Information System to initially extract watershed boundaries. The watershed boundaries are then examined computationally to determine which sections warrant inclusion in the storm surge mesh. Introductory work towards applying image analysis techniques as an alternate means of vertical feature extraction is presented as well. Vertical feature lines extracted from a LiDAR dataset for Manatee County, Florida are included in a limited storm surge finite element mesh for the county and Tampa Bay. Storm surge simulations using the ADCIRC-2DDI model with two meshes, one which includes linear raised features as element edges and one which does not, verify the usefulness of the method.

This thesis presents the development of an automatic mesh generator, named WoodFrameMesh, using object oriented C++. The program developed is capable of generating complete finite element models of wooden houses incorporating frames, linear links, springs, nodal loads and restraints at the desired locations. The finite element mesh generated by the program may be triangular or quadrilateral. The triangular mesh can be generated over any arbitrary domain with multiple openings and line constraints. The program implements the advancing front method for triangulation as discussed by Lee and Hobbs. The difference is made by implementing the algorithm using object oriented concepts and the extensive use of the powerful C++ Standard Template Library (STL). Quadrilateral mesh generation is limited to simple quadrilateral domains with no openings or constraint lines. A simple structured technique is implemented to generate the quadrilateral mesh. The amount of time spent in manual generation of the complete finite element model of wooden houses has been considerably reduced by automating the modeling process. Overall, the use of object oriented design has facilitated the code development and has provided a platform for further additions. The program relies on the use of STL as it provides dynamic data structures, algorithms for storage, searching, sorting, etc. Efficiency of the program is improved by the use of the in-built features in STL instead of developing new code. Analysis of the finite element models generated by the automatic mesh generator is performed using SAP 2000 and WoodFrameSolver. WoodFrameSolver is a finite element analysis engine for WoodFrameMesh, which was developed at Virginia Tech by a group of graduate students (including the author) and professors as a separate project. A chapter discussing the WoodFrameSolver architecture, its extensibility features and its verification is also presented in this thesis. The solver performance and accuracy are similar to those of SAP 2000, which was chosen as the benchmark for testing the analysis results. / Master of Science