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dc.contributor.authorVillena Samson, Michael Daniel
dc.identifier.citationVillena Samson, M. D. (2014). Well-conditioned collocation schemes and new triangular spectral-element methods. Doctoral thesis, Nanyang Technological University, Singapore.
dc.description.abstractIn the first portion of this thesis, a new well-conditioned collocation method for solving differential equations based on Birkhoff interpolation is presented. The collocation schemes on interior points using the interpolation basis functions produce linear systems that do not use differentiation matrices and have coefficient matrices with condition numbers independent of the number of points. The method is extended to different differentiation orders, computational domains and dimensionalities, noting corresponding implementation issues. In the latter portion of this thesis, a new triangular spectral-element method using a recently introduced rectangle-triangle map is presented. This map induces a logarithmic singularity, removed by a fast, stable and accurate numerical algorithm; thus, triangular elements are as efficiently handled as quadrilateral elements. Optimal estimates of approximation by the new modal and nodal bases on a triangle are obtained. Efficient and accurate implementations on one triangle and on an unstructured triangulation of a polygon are demonstrated.en_US
dc.format.extent159 p.en_US
dc.subjectDRNTU::Science::Mathematics::Applied mathematics::Numerical analysisen_US
dc.subjectDRNTU::Science::Mathematics::Applied mathematics::Simulation and modelingen_US
dc.titleWell-conditioned collocation schemes and new triangular spectral-element methodsen_US
dc.contributor.supervisorWang Li-Lianen_US
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US​Doctor of Philosophy (SPMS)en_US
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