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Técnicas para geração de malhas volumétricas não estruturadas podem ser divididas em três categorias principais: técnicas baseadas em Octree, técnica de avanço de fronteira e técnicas Delaunay. Este trabalho faz uso de uma proposta para geração de malhas volumétricas não estruturadas baseada em uma técnica que utiliza uma triangulação adaptativa que contém similaridades com os métodos de geração de malhas baseados em Octree. Esta triangulação, além de decompor o domínio, oferece suporte para a construção de funções implícitas que aproximam a superfície do objeto de interesse. As funções implícitas são obtidas a partir de nuvens de pontos pelo método de Partição da Unidade Implícita - PUI. Um processo de poligonalização discretiza a isosuperfície fornecida pela função implícita gerando uma malha de triângulos superficial. Uma malha volumétrica é gerada a partir da malha superficial utilizando os tetraedros que decompõem o domínio criados pela triangulação. Apresentamos nesta tese um método original para a poligonalização de isosuperfícies obtidas através de nuvens de pontos. Apresentamos também uma abordagem para o melhoramento de malhas volumétricas baseadas na aplicação do conceito de molas virtuais. O foco principal é gerar malhas de qualidade para serem usadas em simulações de fluidos em artérias do corpo humano / Techniques for generation of three-dimensional unstructured meshes can be divided into three main categories: Octree-based techniques, advancing front techniques and Delaunay techniques. In the present study it is used a three-dimensional unstructured mesh generation approach based on a technique which uses an adaptive triangulation which contains similarities with Octree-based mesh generation techniques. This triangulation decomposes the domain and supports the construction of implicit functions that approximates the surface of an object of interest. The implicit functions are derived from point clouds by the Partition of Unity Implicits - PUI method. A polygonization process discretizes the isosurface provided by the implicit function generating a triangular mesh surface. A three-dimensional mesh is generated from the surface mesh using the tetrahedra that decomposes the domain created by the triangulation. In this tesis, we present an original polygonization method of isosurfaces obtained from point clouds. We also present an approach to improve tetrahedral meshes based on the application of the concept of virtual springs. The main focus is to generate quality meshes for fluid flow simulations in human arteries

A new progressive lossy-to-lossless coding method for arbitrarily-connected triangle mesh models of bivariate functions is proposed. The algorithm employs a novel representation of a mesh dataset called a bivariate-function description (BFD) tree, and codes the tree in an efficient manner. The proposed coder yields a particularly compact description of the mesh connectivity by only coding the constrained edges that are not locally preferred Delaunay (locally PD). Experimental results show our method to be vastly superior to previously-proposed coding frameworks for both lossless and progressive coding performance. For lossless coding performance, the proposed method produces the coded bitstreams that are 27.3% and 68.1% smaller than those generated by the Edgebreaker and Wavemesh methods, respectively. The progressive coding performance is measured in terms of the PSNR of function reconstructions generated from the meshes decoded at intermediate stages. The experimental results show that the function approximations obtained with the proposed approach are vastly superior to those yielded with the image tree (IT) method, the scattered data coding (SDC) method, the average-difference image tree (ADIT) method, and the Wavemesh method with an average improvement of 4.70 dB, 10.06 dB, 2.92 dB, and 10.19 dB in PSNR, respectively. The proposed coding approach can also be combined with a mesh generator to form a highly effective mesh-based image coding system, which is evaluated by comparing to the popular JPEG2000 codec for images that are nearly piecewise smooth. The images are compressed with the mesh-based image coder and the JPEG2000 codec at the fixed compression rates and the quality of the resulting reconstructions are measured in terms of PSNR. The images obtained with our method are shown to have a better quality than those produced by the JPEG2000 codec, with an average improvement of 3.46 dB. / Graduate

Técnicas para geração de malhas volumétricas não estruturadas podem ser divididas em três categorias principais: técnicas baseadas em Octree, técnica de avanço de fronteira e técnicas Delaunay. Este trabalho faz uso de uma proposta para geração de malhas volumétricas não estruturadas baseada em uma técnica que utiliza uma triangulação adaptativa que contém similaridades com os métodos de geração de malhas baseados em Octree. Esta triangulação, além de decompor o domínio, oferece suporte para a construção de funções implícitas que aproximam a superfície do objeto de interesse. As funções implícitas são obtidas a partir de nuvens de pontos pelo método de Partição da Unidade Implícita - PUI. Um processo de poligonalização discretiza a isosuperfície fornecida pela função implícita gerando uma malha de triângulos superficial. Uma malha volumétrica é gerada a partir da malha superficial utilizando os tetraedros que decompõem o domínio criados pela triangulação. Apresentamos nesta tese um método original para a poligonalização de isosuperfícies obtidas através de nuvens de pontos. Apresentamos também uma abordagem para o melhoramento de malhas volumétricas baseadas na aplicação do conceito de molas virtuais. O foco principal é gerar malhas de qualidade para serem usadas em simulações de fluidos em artérias do corpo humano / Techniques for generation of three-dimensional unstructured meshes can be divided into three main categories: Octree-based techniques, advancing front techniques and Delaunay techniques. In the present study it is used a three-dimensional unstructured mesh generation approach based on a technique which uses an adaptive triangulation which contains similarities with Octree-based mesh generation techniques. This triangulation decomposes the domain and supports the construction of implicit functions that approximates the surface of an object of interest. The implicit functions are derived from point clouds by the Partition of Unity Implicits - PUI method. A polygonization process discretizes the isosurface provided by the implicit function generating a triangular mesh surface. A three-dimensional mesh is generated from the surface mesh using the tetrahedra that decomposes the domain created by the triangulation. In this tesis, we present an original polygonization method of isosurfaces obtained from point clouds. We also present an approach to improve tetrahedral meshes based on the application of the concept of virtual springs. The main focus is to generate quality meshes for fluid flow simulations in human arteries

Adaptive mesh refinement schemes are used to find accurate low-dimensional approximating spaces when solving elliptic PDEs with Galerkin finite element methods. For nonlinear PDEs, solving the nonlinear problem with Newton's method requires an initial guess of the solution on a refined space, which can be found by interpolating the solution from a previous refinement. Improving the accuracy of the representation of the converged solution computed on a coarse mesh for use as an initial guess on the refined mesh may reduce the number of Newton iterations required for convergence. In this thesis, we present an algorithm to compute an orthogonal L^2 projection between two dimensional finite element spaces constructed from a triangulation of the domain. Furthermore, we present numerical studies that investigate the efficiency of using this algorithm to solve various nonlinear elliptic boundary value problems. / Master of Science

One of the largest sources of error in a CFD simulation is the discretization error. One of the least computationally expensive ways of reducing the discretization error in a simulation is by performing mesh adaptation. In this work, the mesh adaptation processes are driven by the truncation error, which is the local source of the discretization error. Because this work is focused on methods for structured grids, r-adaptation is used as opposed to h-adaptation. A new method for performing the r-adaptation based on an optimization process is developed and presented here. This optimization process was applied to simple 1D and 2D Euler problems as a method of testing the approach. The mesh optimization approach is compared to the more common equidistribution approach to determine which produces more accurate results as well as the costs associated with each. It is found that the optimization process is able to reduce the truncation error than equidistribution. However, in the 2D cases optimization does not reduce the discretization error sufficiently to warrant the significant costs of the approach. This indicates that the much cheaper equidistribution process provides a cost-effective manner to reduce the discretization error in the solution. Further, equidistribution is able to achieve the bulk of the potential reductions in discretization error possible through r-adaptation. This work also develops a new framework for reducing the cost of performing truncation error based r-adaptation. This new framework also addresses some of the issues associated with r-adaptation. In this framework, adaptation is performed on a coarse mesh where it is faster to perform, creating a mapping function for this mesh, and finally evaluating this mapping at a fine enough mesh to meet the error target. The framework is used for 2D Euler and 2D laminar Navier-Stokes problems and shown to be the most cost-effective way to meet a desired error target. Finally, the multi-mesh CFD method is introduced and applied to a wide variety of problems from quasi-1D nozzle to 2D laminar and turbulent boundary layers. The multi-mesh method allows the system of equations to be solved on a system of meshes. With this method, each equation is solved on a mesh that is adapted specifically for it, meaning that more accurate solutions for each equation can be obtained. This work shows that, for certain problems, the multi-mesh approach is able to achieve more accurate results in less time compared to using a single mesh. / Doctor of Philosophy / Computational fluid dynamics (CFD) describes a method of numerically solving equations that attempt to model the behavior of a fluid. As computers have become cheaper and more powerful and the software has become more capable, CFD has become an integral part of the engineering process. One of the goals of the field is to be able to bring these higher fidelity simulations into the design loop earlier. Ideally, using CFD earlier in the design process would allow design engineers to create new innovative designs with less programmatic risk. Likewise, it is also becoming necessary to use these CFD tools later in the final design process to replace some physical experiments which can be expensive, unsafe, or infeasible to run. Both of these goals require the CFD codes to meet the accuracy requirements for the results as fast as possible. This work discusses several different methods for improving the accuracy of the simulations as well as ways of obtaining these more accurate results for the cheapest cost. In CFD, the governing equations modeling the flow behavior are solved on a computer. As a result, these continuous differential equations must be approximated as a system of discrete equations, so that they can be solved on a computer. These approximations result in discretization error, the difference between the exact solutions to the discrete and continuous equations, which is typically the largest type of numerical error in a CFD solution. The source of the discretization error is the truncation error, which is composed of the terms left out of the approximations made when discretizing the continuous equations. Thus, if the truncation error can be reduced, the discretization error in the solution should also be reduced. In this work, several different ways of reducing this truncation error through mesh adaptation are discussed, including the use of optimization methods. These mesh optimization methods are compared to a more common way of performing adaptation, namely equidistribution. It is determined that equidistribution is able to reduce the discretization error by a similar amount while being significantly faster than mesh optimization. This work also presents a framework for making the adaptation process faster overall by performing the adaptation on a coarse mesh and then refining the mesh enough to meet the error tolerance for the application. This framework was the cheapest method investigated to meet a given error target. This work also introduces a new technique called multi-mesh CFD, which allows each equation (conservation of mass, momentum, energy, etc.) to be solved on a separate mesh. This allows each equation to be solved on a mesh that is specifically adapted for it, resulting in a more accurate solution. Here, it is shown that, for certain problems, the multi-mesh technique is able to obtain a solution with lower error than only using a single mesh. This work also shows that these more accurate results can be obtained in less time using multiple meshes than on a single mesh.

ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, California / The purpose of this paper is to explain the process to implementing a wireless sensor network in order to improve situational awareness in a dense urban environment. Utilizing a system of wireless nodes with Global Positioning System (GPS) and heart rate sensors, a system was created that was able to give both position and general health conditions. By linking the nodes in a mesh network line of sight barriers were overcome to allow for operation even in an environment full of obstruction.

Internet of Things (iot) is a growing field enabled by many different technologies. One of these technologies is  Bluetooth Low Energy (ble). It is of interest to investigate the potential of ble and one interesting, currently unsupported, feature is mesh networking. This thesis work aims to investigate whether it is possible to design and implement a mesh network protocol using ble. To verify the implemented mesh network protocols functionality an indoor localization system has been implemented upon the BLE mesh network protocol. Furthermore this thesis work investigates if an indoor localization system can benefit from using a mesh network. The results of the investigation is a proof of concept of a functional ble mesh network protocol implemented on hardware and tested in a real environment. Tests show that the implemented localization system has similar accuracy as other rssi based indoor localization systems. The largest advantage found for a mesh based indoor localization is the ability to localize objects outside of the radio propagation range of the user. This feature is enabled by multi-hop messaging in the mesh network.

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