Abstract
In this paper, we give an overview of multigrid methods for two systems of equations, namely the Stokes equations and the incompressible poroelasticity equations. We emphasize the saddle point type aspect in these two systems and discuss their discretization on staggered and collocated grids. The basic problem is that of smoothing a system of equations that has a zero (or almost zero) block in the matrix for one of the unknowns. In particular, we discuss the coupled relaxation approach, with its "box-wise" and "line-wise" versions and distributive relaxation, that gives a decoupled system of equations for smoothing. For general systems of equations it is a challenge to design an efficient distributive relaxation scheme. This paper may help in finding one.
Original language | English |
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Pages (from-to) | 1933-1950 |
Number of pages | 18 |
Journal | Applied Numerical Mathematics |
Volume | 58 |
Issue number | 12 |
DOIs | |
Publication status | Published - Dec 2008 |
Externally published | Yes |
Bibliographical note
Funding Information:✩ This research has been partially supported by the Dutch government through the national program BSIK: knowledge and research capacity, in the ICT project BRICKS (http://www.bsik-bricks.nl), theme MSV1, and by the INTAS project 03-50-4395, the Spanish project MEC/FEDER MTM 2004-019051 and the Diputación General de Aragón. * Corresponding author. E-mail addresses: [email protected] (C.W. Oosterlee), [email protected] (F.J. Gaspar).
Funding
✩ This research has been partially supported by the Dutch government through the national program BSIK: knowledge and research capacity, in the ICT project BRICKS (http://www.bsik-bricks.nl), theme MSV1, and by the INTAS project 03-50-4395, the Spanish project MEC/FEDER MTM 2004-019051 and the Diputación General de Aragón. * Corresponding author. E-mail addresses: [email protected] (C.W. Oosterlee), [email protected] (F.J. Gaspar).
Keywords
- Collocated grid
- Coupled relaxation
- Distributive relaxation
- Multigrid
- Poroelasticity
- Staggered grid
- Stokes equations
- System transformation