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dc.contributor.authorHalliwell, Garry T.
dc.date.accessioned2016-04-05T19:13:09Z
dc.date.available2016-04-05T19:13:09Z
dc.date.issued2013
dc.identifier.isbn9781267946034
dc.identifier.other1316918872
dc.identifier.urihttp://hdl.handle.net/10477/50533
dc.description.abstractMathematical models for thin-film evolution equations and their coarsening behavior have been extensively studied, however a challenge for computer simulations is finding time stepping algorithms that evolve large systems to long times. The thin solid film model is a nonlinear, fourth order, parabolic partial differential equation that is first order in time. Using a semi-implicit operator splitting spectral method, we developed an algorithm that is unconditionally stable allowing arbitrarily large time steps. Stability was achieved by von Neumann analysis resulting in an adaptive parametrization of the splitting at each time step. The novel aspect of this work relative to similar work done on other coarsening models, e.g. the Cahn-Hilliard equation, is the treatment of non-local and inverse power terms. Our numerical method is robust and accurate, with coarsening results orders of magnitude shorter in computation time than Euler's Method.
dc.languageEnglish
dc.sourceDissertations & Theses @ SUNY Buffalo,ProQuest Dissertations & Theses Global
dc.subjectPure sciences
dc.subjectApplied sciences
dc.subjectApplied physics
dc.subjectMathematics
dc.subjectNumerical analysis
dc.subjectQuantum dots
dc.subjectQuantum wires
dc.subjectThin-films
dc.titleAn unconditionally stable spectral method for an isotropic thin-film equation
dc.typeDissertation/Thesis


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