Low-order preconditioning of the Stokes equations

by   Alexey Voronin, et al.

Low-order finite-element discretizations are well-known to provide effective preconditioners for the linear systems that arise from higher-order discretizations of the Poisson equation. In this work, we show that high-quality preconditioners can also be derived for the Taylor-Hood discretization of the Stokes equations in much the same manner. In particular, we investigate the use of geometric multigrid based on the ℚ_1isoℚ_2/ ℚ_1 discretization of the Stokes operator as a preconditioner for the ℚ_2/ℚ_1 discretization of the Stokes system. We utilize local Fourier analysis to optimize the damping parameters for Vanka and Braess-Sarazin relaxation schemes and to achieve robust convergence. These results are then verified and compared against the measured multigrid performance. While geometric multigrid can be applied directly to the ℚ_2/ℚ_1 system, our ultimate motivation is to apply algebraic multigrid within solvers for ℚ_2/ℚ_1 systems via the ℚ_1isoℚ_2/ ℚ_1 discretization, which will be considered in a companion paper.



There are no comments yet.


page 1


Higher order Trace Finite Element Methods for the Surface Stokes Equation

In this paper a class of higher order finite element methods for the dis...

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

We present a matrix-free flow solver for high-order finite element discr...

A Large-Scale Benchmark for the Incompressible Navier-Stokes Equations

We introduce a collection of benchmark problems in 2D and 3D (geometry d...

Variational discretization of the Navier-Stokes-Fourier system

This paper presents the variational discretization of the compressible N...

Monolithic multigrid for a reduced-quadrature discretization of poroelasticity

Advanced finite-element discretizations and preconditioners for models o...

Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs

The Poisson pressure solve resulting from the spectral element discretiz...

Robust monolithic solvers for the Stokes-Darcy problem with the Darcy equation in primal form

We construct mesh-independent and parameter-robust monolithic solvers fo...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.