Distributive smoothers in multigrid for problems with dominating grad-div operators

被引：19

作者：

Gaspar, F. J. ^{[1
]}

Gracia, J. L. ^{[1
]}

Lisbona, F. J. ^{[1
]}

Osterlee, C. W. ^{[2
,3
]}

机构：

[1] Univ Zaragoza, Dept Appl Math, Ctr Politecn Super, Zaragoza 50018, Spain

[2] CWI Ctr Math & Comp Sci, Amsterdam, Netherlands

[3] Delft Univ Technol, Delft Inst Appl Math, Delft, Netherlands

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2008年 / 15卷 / 08期

关键词：

multigrid; distributive smoothing; grad-div operator; staggered grid; poro-elasticity;

D O I：

10.1002/nla.587

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present efficient multigrid methods for systems of partial differential equations that are governed by a dominating grad-div operator. In particular, we show that distributive smoothing methods give multigrid convergence factors that are independent of problem parameters and of the mesh sizes in space and time. The applications range from model problems to secondary consolidation Biot's model. We focus oil the smoothing issue and mainly solve academic problems on Cartesian-staggered grids. Copyright (C) 2008 John Wiley & Sons, Ltd.

引用

页码：661 / 683

页数：23

共 42 条

[11] On convergence of certain finite volume difference discretizations for 1D poroelasticity interface problems [J].

Ewing, Richard E. ;

Iliev, Oleg P. ;

Lazarov, Raytcho D. ;

Naumovich, Anna .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2007, 23 (03) :652-671

[12] A stabilized method for a secondary consolidation Biot's model [J].

Gaspar, F. J. ;

Gracia, J. L. ;

Lisbona, F. J. ;

Vabishchevich, P. N. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (01) :60-78

[13] An efficient multigrid solver for a reformulated version of the poroelasticity system [J].

Gaspar, F. J. ;

Lisbona, F. J. ;

Oosterlee, C. W. ;

Vabishchevich, P. N. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (08) :1447-1457

[14] A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods [J].

Gaspar, F. J. ;

Lisbona, F. J. ;

Oosterlee, C. W. .

COMPUTING AND VISUALIZATION IN SCIENCE, 2008, 11 (02) :67-76

[15] A finite difference analysis of Biot's consolidation model [J].

Gaspar, FJ ;

Lisbona, FJ ;

Vabishchevich, PN .

APPLIED NUMERICAL MATHEMATICS, 2003, 44 (04) :487-506

[16] A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system [J].

Gaspar, FJ ;

Lisbona, FJ ;

Oosterlee, CW ;

Wienands, R .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2004, 11 (2-3) :93-113

[17] Staggered grid discretizations for the quasi-static Biot's consolidation problem [J].

Gaspar, FJ ;

Lisbona, FJ ;

Vabishchevich, PN .

APPLIED NUMERICAL MATHEMATICS, 2006, 56 (06) :888-898

[18] Multilevel methods for mixed finite elements in three dimensions [J].

Hiptmair, R ;

Hoppe, RHW .

NUMERISCHE MATHEMATIK, 1999, 82 (02) :253-279

[19] The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods [J].

Hyman, J ;

Shashkov, M ;

Steinberg, S .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 42 (12) :1527-1547

[20] Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids [J].

Hyman, JM ;

Shashkov, M .

APPLIED NUMERICAL MATHEMATICS, 1997, 25 (04) :413-442

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