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Distributive smoothers in multigrid for problems with dominating grad–div operators
Author(s) -
Gaspar F. J.,
Gracia J. L.,
Lisbona F. J.,
Oosterlee C. W.
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.587
Subject(s) - multigrid method , smoothing , mathematics , distributive property , polygon mesh , partial differential equation , discretization , biot number , mathematical optimization , convergence (economics) , mathematical analysis , pure mathematics , geometry , statistics , physics , economics , economic growth , mechanics
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 on the smoothing issue and mainly solve academic problems on Cartesian‐staggered grids. Copyright © 2008 John Wiley & Sons, Ltd.