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Kronecker Product Approximation Preconditioners for Convection-diffusion Model Problems

Laura Grigori 1 Hua Xiang 2, *
* Corresponding author
1 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : We consider the iterative solution of the linear systems arising from four convection-diffusion model problems: the scalar convection-diffusion problem, Stokes problem, Oseen problem, and Navier-Stokes problem. We give the explicit Kronecker product structure of the coefficient matrices, especially the Kronecker product structure for the convection term. For the latter three model cases, the coefficient matrices have a $2 \times 2$ blocks, and each block is a Kronecker product or a summation of several Kronecker products. We use the Kronecker products and block structures to design the diagonal block preconditioner, the tridiagonal block preconditioner and the constraint preconditioner. We can find that the constraint preconditioner can be regarded as the modification of the tridiagonal block preconditioner and the diagonal block preconditioner based on the cell Reynolds number. That's the reason why the constraint preconditioner is usually better. We also give numerical examples to show the efficiency of this kind of Kronecker product approximation preconditioners.
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https://hal.inria.fr/inria-00268301
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Submitted on : Monday, May 19, 2008 - 10:27:45 AM
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Laura Grigori, Hua Xiang. Kronecker Product Approximation Preconditioners for Convection-diffusion Model Problems. [Technical Report] RR-6536, INRIA. 2008. ⟨inria-00268301v5⟩

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