Augmented Lagrangian-based preconditioners for steady buoyancy driven flow
| Autor: | Geoffrey Dillon, Guoyi Ke, Eugenio Aulisa, Victoria E. Howle |
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| Rok vydání: | 2018 |
| Předmět: |
Augmented Lagrangian method
Preconditioner Applied Mathematics Prandtl number 010103 numerical & computational mathematics Rayleigh number Solver Computer Science::Numerical Analysis 01 natural sciences Generalized minimal residual method Mathematics::Numerical Analysis 010101 applied mathematics symbols.namesake Rate of convergence Flow (mathematics) Computer Science::Mathematical Software symbols Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematics Letters. 82:1-7 |
| ISSN: | 0893-9659 |
| Popis: | In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable’s order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable. |
| Databáze: | OpenAIRE |
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