Geometric aspects of local adaptive Galerkin bases.
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
The local adaptive Galerkin bases for large dynamical systems, whose long time behaviour is confined to a finite dimensional manifold, are bases chosen by a local version of a singular value decomposition analysis. We show that these bases are picked out by choosing directions of maximum bending of the manifold. We discover a useful way to compute the dimension and local shape of the manifold. The application of the results is evaluated by examining numerically several interesting examples.Type
textDissertation-Reproduction (electronic)
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Applied MathematicsGraduate College