347 research outputs found

    TetGen, towards a quality tetrahedral mesh generator

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    TetGen is a C++ program for generating quality tetrahedral meshes aimed to support numerical methods and scientific computing. It is also a research project for studying the underlying mathematical problems and evaluating algorithms. This paper presents the essential meshing components developed in TetGen for robust and efficient software implementation. And it highlights the state-of-the-art algorithms and technologies currently implemented and developed in TetGen for automatic quality tetrahedral mesh generation

    State of the Art: Updating Delaunay Triangulations for Moving Points

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    This paper considers the problem of updating efficiently a two-dimensional Delaunay triangulation when vertices are moving. We investigate the three current state-of-the-art approaches to solve this problem: --1-- the use of kinetic data structures, --2-- the possibility of moving points from their initial to final position by deletion and insertion and --3-- the use of "almost" Delaunay structure that postpone the necessary modifications. Finally, we conclude with a global overview of the above-mentioned approaches while focusing on future works

    Nature of the learning algorithms for feedforward neural networks

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    The neural network model (NN) comprised of relatively simple computing elements, operating in parallel, offers an attractive and versatile framework for exploring a variety of learning structures and processes for intelligent systems. Due to the amount of research developed in the area many types of networks have been defined. The one of interest here is the multi-layer perceptron as it is one of the simplest and it is considered a powerful representation tool whose complete potential has not been adequately exploited and whose limitations need yet to be specified in a formal and coherent framework. This dissertation addresses the theory of generalisation performance and architecture selection for the multi-layer perceptron; a subsidiary aim is to compare and integrate this model with existing data analysis techniques and exploit its potential by combining it with certain constructs from computational geometry creating a reliable, coherent network design process which conforms to the characteristics of a generative learning algorithm, ie. one including mechanisms for manipulating the connections and/or units that comprise the architecture in addition to the procedure for updating the weights of the connections. This means that it is unnecessary to provide an initial network as input to the complete training process.After discussing in general terms the motivation for this study, the multi-layer perceptron model is introduced and reviewed, along with the relevant supervised training algorithm, ie. backpropagation. More particularly, it is argued that a network developed employing this model can in general be trained and designed in a much better way by extracting more information about the domains of interest through the application of certain geometric constructs in a preprocessing stage, specifically by generating the Voronoi Diagram and Delaunav Triangulation [Okabe et al. 92] of the set of points comprising the training set and once a final architecture which performs appropriately on it has been obtained, Principal Component Analysis [Jolliffe 86] is applied to the outputs produced by the units in the network's hidden layer to eliminate the redundant dimensions of this space

    Doctor of Philosophy

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    dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains
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