Adaptive Techniques Applied to the Sequentially Optimized Meshfree Approximation

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dc.contributor.advisorAkin, John Edward.
dc.contributor.committeeMemberStanciulescu, Ilinca
dc.contributor.committeeMemberMeade, Andrew J., Jr.
dc.creatorMittelman, Rachel
dc.date.accessioned2014-09-22T20:31:08Z
dc.date.available2014-09-22T20:31:08Z
dc.date.created2014-05
dc.date.issued2014-04-22
dc.date.submittedMay 2014
dc.date.updated2014-09-22T20:31:08Z
dc.description.abstractThis thesis advances the meshless Sequentially Optimized Meshfree Approximation (SOMA) from a fixed grid to an adaptive one by applying residual-based adaptive techniques. In its fixed grid form, SOMA constructs an approximation of an equation solution using optimized radial basis functions (RBFs), but deletes the RBF parameters once each basis function is appropriately added. The first proposed method saves this information, constructs an approximation of the solution, and intelligently adds points to the problem domain. The second proposed method is a flexible interpolation scheme which does not require this basis saving technique, although the two techniques can be combined. When applied to various equations, these adaptive algorithms demonstrate the convergence required to achieve a satisfactory level of precision, saving time and computational effort for the same mathematical result as a denser grid. Applications of this algorithm include function approximation as well as differential equations which demonstrate its capability and robustness.
dc.format.mimetypeapplication/pdf
dc.identifier.citationMittelman, Rachel. "Adaptive Techniques Applied to the Sequentially Optimized Meshfree Approximation." (2014) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77224">https://hdl.handle.net/1911/77224</a>.
dc.identifier.urihttps://hdl.handle.net/1911/77224
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectAdaptive mesh refinement
dc.subjectCollocation methods
dc.titleAdaptive Techniques Applied to the Sequentially Optimized Meshfree Approximation
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMechanical Engineering and Materials Science
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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