Rees, Glyn and Silvester, David and Mihajlovic, Milan (2011) A truncated ILU smoother for multigrid preconditioning of convection dominated flow problems. [MIMS Preprint]
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Abstract
Multigrid methods are known to be efficient preconditioners and solvers for linear systems obtained from discretizing second-order, scalar elliptic problems. Singular perturbations involving these problems (such as the convection-diffusion equation) introduce new properties into the discrete problem, and this typically leads to the deterioration in the effectiveness of multigrid methods using standard point smoothers when close to the perturbation limit. In this paper we propose a new smoothing strategy, based on incomplete factorisation of truncated matrices arizing in the multigrid hierarchy. The truncation procedure is based on the heuristics used to determine strong connections in the classical (Ruge-Stuben) algebraic multigrid method. We report results of tests of the new smoother both for geometric and for algebraic multigrid on benchmark problems in two and three spatial dimensions.
| Item Type: | MIMS Preprint |
|---|---|
| Uncontrolled Keywords: | convection-diffusion, preconditioning, incomplete factorisation, multigrid, |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | professor david silvester |
| Date Deposited: | 23 Apr 2011 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1487 |
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