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oai:drum.lib.umd.edu:1903/87432016-03-29T06:34:09Zcom_1903_2224com_1903_12com_1903_2261com_1903_2col_1903_2756col_1903_2793col_1903_3

Elman, Howard Deane, Anil Lott, Paul Aaron Digital Repository at the University of Maryland University of Maryland (College Park, Md.) Applied Mathematics and Scientific Computation 2009-01-24T06:34:14Z 2009-01-24T06:34:14Z 2008-09-02 http://hdl.handle.net/1903/8743 We 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. 6573815 bytes application/pdf en_US Fast Solvers for Models of Fluid Flow with Spectral Elements Dissertation Mathematics Computer Science Mathematics Computational Fluid Dynamics Navier-Stokes Convection-Diffusion Spectral Element Method open.access