Multigrid relaxation methods for systems of saddle point type

Authors:
C. W. Oosterlee;F. J. Gaspar
Affiliations:
CWI, Center for Mathematics and Computer Science, Amsterdam, the Netherlands and Delft University of Technology, Delft Institute of Applied Mathematics (DIAM), the Netherlands;Departamento de Mathemática Aplicada, University of Zaragoza, Zaragoza, Spain
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 22
Cited 0

Block-implicit multigrid solution of Navier-Stokes equations in primitive variables

Journal of Computational Physics
A second-order accurate pressure correction scheme for viscous incompressible flow

SIAM Journal on Scientific and Statistical Computing
On the robustness of Ilu smoothing

SIAM Journal on Scientific and Statistical Computing
An adaptive multigrid technique for the incompressible Navier-Stokes equations

Journal of Computational Physics
Analysis of a multigrid Stokes solver

Applied Mathematics and Computation
Accelerated multigrid convergence and high-Reynolds recirculating flows

SIAM Journal on Scientific Computing
A robust multigrid method for a discretization of the incompressible Navier-Stokes equations in general coordinates

IMPACT of Computing in Science and Engineering
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes

Mathematics of Computation
An efficient smoother for the Stokes problem

Applied Numerical Mathematics - Special issue on multilevel methods
A numerical method for solving incompressible viscous flow problems

Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Adjoint operators for the natural discretizations of the divergence gradient and curl on logically rectangular grids

Applied Numerical Mathematics
Comparison of multigrid methods for neutral and stably stratified flows over two-dimensional obstacles

Journal of Computational Physics
Computing flows on general three-dimensional nonsmooth staggered grids

Journal of Computational Physics
A multigrid tutorial: second edition

A multigrid tutorial: second edition
Geometric multigrid with applications to computational fluid dynamics

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid

Multigrid
Automated Transformations for PDE Systems with Application to Multigrid Solvers

SIAM Journal on Scientific Computing
Symmetry-preserving discretization of turbulent flow

Journal of Computational Physics
An Efficient Multigrid Solver based on Distributive Smoothing for Poroelasticity Equations

Computing
Staggered grid discretizations for the quasi-static Biot's consolidation problem

Applied Numerical Mathematics
Principles of Computational Fluid Dynamics

Principles of Computational Fluid Dynamics
A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods

Computing and Visualization in Science

Quantified Score

Hi-index	0.00

Visualization

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.