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Title: Well-conditioned collocation schemes and new triangular spectral-element methods
Authors: Villena Samson, Michael Daniel
Keywords: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
Issue Date: 2014
Source: Villena Samson, M. D. (2014). Well-conditioned collocation schemes and new triangular spectral-element methods. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: In 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.
DOI: 10.32657/10356/60760
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Theses

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