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Kernel-Based Meshless Methods

Show simple item record Corrigan, Andrew
dc.creator Corrigan, Andrew 2009-04-30 2009-07-25T20:41:58Z NO_RESTRICTION en 2009-07-25T20:41:58Z 2009-07-25T20:41:58Z
dc.description.abstract In order to improve their applicability as a tool for solving partial differential equations in computational science, we equip kernel-based meshless methods with a number of new capabilities. First, we provide kernel-based meshless methods with the first wellposed, general technique which allows for adaptively-scaled trial functions. This is done by constructing an adaptively-scaled kernel which maintains positive definiteness. We extend sampling inequalities to optimally bound fractional order Sobolev norms in terms of possibly higher order data. This sampling inequality is then applied to obtain more optimal error bounds in a reformulation of Schaback’s framework for unsymmetric meshless methods. We provide kernel-based meshless methods with a direct visualization technique, by adapting Fourier volume rendering to deal directly with meshless data, which was previously only used directly for grid-based data. Modern graphics hardware has emerged as a powerful architecture for scientific computing. We implement an unstructured grid-based inviscid, compressible flow solver on modern graphics hardware, and obtain an order of magnitude speed-up in comparison to an equivalent code running on a quad-core CPU.
dc.language.iso en_US en
dc.subject Meshless Methods en_US
dc.subject Sampling Inequality en_US
dc.subject Graphics Hardware en_US
dc.subject Kernel Method en_US
dc.subject Volume Rendering en_US
dc.subject Computational Fluid Dynamics en_US
dc.title Kernel-Based Meshless Methods en
dc.type Dissertation en Doctor of Philosophy in Computational Science and Informatics en Doctoral en Computational Sciences and Informatics en George Mason University en

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