311 research outputs found

    Parametric Interpolation To Scattered Data [QA281. A995 2008 f rb].

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    Dua skema interpolasi berparameter yang mengandungi interpolasi global untuk data tersebar am dan interpolasi pengekalan-kepositifan setempat data tersebar positif dibincangkan. Two schemes of parametric interpolation consisting of a global scheme to interpolate general scattered data and a local positivity-preserving scheme to interpolate positive scattered data are described

    High-order adaptive methods for computing invariant manifolds of maps

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    The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar maps. Next, he develops and tests the method for parametric surfaces and then he adapts this method to invariant manifolds of three-dimensional maps

    Numerical simulations of fuel droplet flows using a Lagrangian triangular mesh

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    The incompressible, Lagrangian, triangular grid code, SPLISH, was converted for the study of flows in and around fuel droplets. This involved developing, testing and incorporating algorithms for surface tension and viscosity. The major features of the Lagrangian method and the algorithms are described. Benchmarks of the algorithms are given. Several calculations are presented for kerosene droplets in air. Finally, extensions which make the code compressible and three dimensional are discussed

    Arbitrary topology meshes in geometric design and vector graphics

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    Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

    Convergence of adaptive stochastic collocation with finite elements

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    We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an adaptive algorithm which adaptively enriches the parameter space as well as refines the finite element meshes

    Convergence of adaptive stochastic collocation with finite elements

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    We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes

    Unstructured mesh generation for mesh improvement techniques and contour meshing.

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    This thesis will investigate surface mesh generation and develop ideas to improve the quality of surface meshes that are currently produced. Surface geometries are represented by a CAD definition, but the CAD definition does not necessarily guarantee that the surface geometry is acceptable for mesh generation. CAD geometries will often contain a number of detailed features which will need to be improved by processes such as CAD repair before mesh generation can take place. Even then the geometries can still contain problems in the features such as, small sliver surface patches and sliver edges. These features cause major difficulties when meshed, as they generate small distorted elements. Here we will look to improve the meshes by merging together neighboring surface patches to create a super patch and then generate the mesh on this one surface. The merging of surfaces is controlled by the angle between surface patches. Another method that will be investigated involves the re-meshing of the geometry based on a prescribed metric. In addition to looking at this problem of CAD representation we will also look at the growing area of medical imaging. Here we will look to produce a 3D mesh from a set of contours. From this the mesh produced will be remeshed using the previous ideas to produce a mesh that can be used for analysis
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