2006
DOI: 10.1137/040608817
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Block Preconditioners Based on Approximate Commutators

Abstract: This paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible Navier-Stokes equations. We consider the "pressure convectiondiffusion preconditioners" proposed by Kay, Loghin, and Wathen [SIAM

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Cited by 159 publications
(154 citation statements)
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“…Therefore, Q −1 u is replaced witĥ Q −1 u , the inverse of the diagonal of the velocity mass matrix. According to the literature ( [13], [11]), the convergence of the LSC and PCD preconditioners is independent of the grid size, and only mildly dependent on the Reynolds number. The preconditioners have been tested for the driven cavity and backward facing step problem using Q2-Q1 and Q2-P1 elements.…”
Section: Preconditioning Strategies Based On Block Factorizationmentioning
confidence: 99%
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“…Therefore, Q −1 u is replaced witĥ Q −1 u , the inverse of the diagonal of the velocity mass matrix. According to the literature ( [13], [11]), the convergence of the LSC and PCD preconditioners is independent of the grid size, and only mildly dependent on the Reynolds number. The preconditioners have been tested for the driven cavity and backward facing step problem using Q2-Q1 and Q2-P1 elements.…”
Section: Preconditioning Strategies Based On Block Factorizationmentioning
confidence: 99%
“…From the eigenvalues, it is evident that convergence with the preconditioners based on formulation (5) depends strongly on the approximation to the Schur complement matrix. In ( [11], [10], [13]) one can find examples of such preconditioners.…”
Section: Preconditioning Strategies Based On Block Factorizationmentioning
confidence: 99%
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“…whereŜ is approximated by a least squares commutator approach [10]. The approximation is based on commutator of the convection diffusion operator (on the velocity and pressure space) with the gradient operator.…”
Section: Lsc Preconditionermentioning
confidence: 99%