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Type of Document	Dissertation
Author	Reyna, Luis Guillermo M.
URN	etd-06222005-104752
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-06222005-104752
Title	I. Stability of Tchebyshev collocation. II. Interpolation for surfaces with 1-D discontinuities. III. On composite meshes
Degree	PhD
Option	Applied and Computational Mathematics
Advisory Committee	Advisor Name Title Heinz-Otto Kreiss Committee Chair
Keywords	none
Date of Defense	1982-10-15
Availability	restricted
Abstract I. Stability of Tchebyshev Collocation We describe Tchebyshev collocation when applied to hyperbolic equations in one space dimension. We discuss previous stability results valid for scalar equations and study a procedure that when applied to a strictly hyperbolic system of equations leads to a stable numerical approximation in the L2-norm. The method consists of using orthogonal projections in the L2-norm to apply the boundary conditions and smooth the higher modes. II. On 2-D Interpolation for Surfaces with 1-D Discontinuities This problem arises in the context of shock calculations in two space dimensions. Given the set of parabolic equations describing the shock phenomena the method proceeds by discretising in time and then solving the resulting elliptic equation by splitting. The specific problem is to reconstruct a two dimensional function which is fully resolved along a few parallel horizontal lines. The interpolation proceeds by determining the position of any discontinuity and then interpolating parallel to it. III. On Composite Meshes We collect several numerical experiments designed to determine possible numerical artifacts produced by the overlapping region of composite meshes. We also study the numerical stability of the method when applied to hyperbolic equations. Finally we apply it to a model of a wind driven ocean circulation model in a circular basin. We use stretching in the angular and radial directions which allow the necessary resolution to be obtained along the boundary.
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