Fast Solvers for Models of Fluid Flow with Spectral Elements

We present a preconditioning approach in accordance with Domain Decomposition and the Fast Diagonalization Method which could be used on tensor product based discretizations of the steady convection-diffusion and the linearized Navier-Stokes equations. The technique depends on iterative substructuring where fast diagonalization is utilized to effectively get rid of the interior degrees of freedom and subsidiary subdomain solves. We show the strength of this preconditioner in numerical simulations utilizing a spectral element discretization. This report expands the use of Fast Diagonalization to steady convection-diffusion systems. We also extend the “least-squares commutator” preconditioner, initially produced for the finite element method, to a matrix-free spectral element framework. We reveal that both of these advances, whenever used collectively, enable effective computation of steady-state solutions the the incompressible Navier-Stokes equations using high-order spectral element discretizatio…

Source: University of Maryland

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