Block preconditioners based on approximate commutators

被引:125
作者
Elman, H [1 ]
Howle, VE
Shadid, J
Shuttleworth, R
Tuminaro, R
机构
[1] Univ Maryland, Dept Comp Sci, College Pk, MD 20742 USA
[2] Univ Maryland, Inst Adv Comp Studies, College Pk, MD 20742 USA
[3] Sandia Natl Labs, Livermore, CA 94551 USA
[4] Univ Maryland, Appl Math & Sci Comp Program, College Pk, MD 20742 USA
关键词
preconditioning; Navier-Stokes; iterative algorithms;
D O I
10.1137/040608817
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible Navier-Stokes equations. We consider the "pressure convection diffusion preconditioners" proposed by Kay, Loghin, and Wathen [SIAM J. Sci. Comput., 24 (2002), pp. 237-256] and Silvester, Elman, Kay, and Wathen [J. Comput. Appl. Math., 128 (2001), pp. 261-279]. Numerous theoretical and numerical studies have demonstrated mesh independent convergence on several problems and the overall efficacy of this methodology. A drawback, however, is that it requires the construction of a convection-diffusion operator (denoted F-p) projected onto the discrete pressure space. This means that integration of this idea into a code that models incompressible flow requires a sophisticated understanding of the discretization and other implementation issues, something often held only by the developers of the model. As an alternative, we consider automatic ways of computing F-p based on purely algebraic considerations. The new methods are closely related to the "BFBt preconditioner" of Elman [SIAM J. Sci. Comput., 20 (1999), pp. 1299-1316]. We use the fact that the preconditioner is derived from considerations of commutativity between the gradient and convection-diffusion operators, together with methods for computing sparse approximate inverses, to generate the required matrix F-p automatically. We demonstrate that with this strategy the favorable convergence properties of the preconditioning methodology are retained.
引用
收藏
页码:1651 / 1668
页数:18
相关论文
共 19 条
[1]  
Benson MW., 1982, Utilitas Math, V22, P127
[2]  
BENSON MW, 1973, THESIS LAKEHEAD U TH
[4]   A priori sparsity patterns for parallel sparse approximate inverse preconditioners [J].
Chow, E .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (05) :1804-1822
[5]  
CHOW E, 1994, 94101 UMSI
[6]   Preconditioning for the steady-state Navier-Stokes equations with low viscosity [J].
Elman, HC .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 20 (04) :1299-1316
[7]  
ELMAN HC, INCOMPRESSIBLE FLOW
[8]  
ELMAN HC, 2005, IN PRESS FINITE ELEM
[9]   Parallel preconditioning with sparse approximate inverses [J].
Grote, MJ ;
Huckle, T .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1997, 18 (03) :838-853
[10]   NUMERICAL CALCULATION OF TIME-DEPENDENT VISCOUS INCOMPRESSIBLE FLOW OF FLUID WITH FREE SURFACE [J].
HARLOW, FH ;
WELCH, JE .
PHYSICS OF FLUIDS, 1965, 8 (12) :2182-&