Low-order preconditioning of the Stokes equations

03/22/2021
by   Alexey Voronin, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

09/18/2019

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...
10/07/2019

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...
12/10/2021

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

We introduce a collection of benchmark problems in 2D and 3D (geometry d...
02/07/2022

Variational discretization of the Navier-Stokes-Fourier system

This paper presents the variational discretization of the compressible N...
07/08/2021

Monolithic multigrid for a reduced-quadrature discretization of poroelasticity

Advanced finite-element discretizations and preconditioners for models o...
10/14/2021

Tuning Spectral Element Preconditioners for Parallel Scalability on GPUs

The Poisson pressure solve resulting from the spectral element discretiz...
10/14/2021

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.