Fast Solvers for Models of Fluid Flow with Spectral Elements

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dc.contributor.advisorElman, Howarden_US
dc.contributor.advisorDeane, Anilen_US
dc.contributor.authorLott, Paul Aaronen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2009-01-24T06:34:14Z
dc.date.available2009-01-24T06:34:14Z
dc.date.issued2008-09-02en_US
dc.description.abstractWe introduce a preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The method is based on iterative substructuring where fast diagonalization is used to efficiently eliminate the interior degrees of freedom and subsidiary subdomain solves. We demonstrate the effectiveness of this preconditioner in numerical simulations using a spectral element discretization. This work extends the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the "least-squares commutator" preconditioner, originally developed for the finite element method, to a matrix-free spectral element framework. We show that these two advances, when used together, allow for efficient computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizations.en_US
dc.format.extent6573815 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/8743
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledComputer Scienceen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledComputational Fluid Dynamicsen_US
dc.subject.pquncontrolledNavier-Stokesen_US
dc.subject.pquncontrolledConvection-Diffusionen_US
dc.subject.pquncontrolledSpectral Element Methoden_US
dc.titleFast Solvers for Models of Fluid Flow with Spectral Elementsen_US
dc.typeDissertationen_US

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