Title: COMPUTING STEADY FLOW STATES USING FAST ITERATIVE SOLVERS
P. Aaron Lott, Howard Elman, Anil Deane and Jeff McFadden
Affiliation: ITL/MCSD, NIST Gaithersburg, MD 20899.
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 equation 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 to the incompressible Navier-Stokes equations using high-order spectral element discretizations.
Mentors Name: Jeff McFadden
Building 225, Room B166, Stop 8910
Authors Name: P. Aaron Lott
Building 225, Room B155, Stop 8910
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