Name
Abstract | ||
|---|---|---|
A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. 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 DOUBLE-STRUCK CAPITAL Q1isoDOUBLE-STRUCK CAPITAL Q2/DOUBLE-STRUCK CAPITAL Q1 discretization of the Stokes operator as a preconditioner for the DOUBLE-STRUCK CAPITAL Q2/DOUBLE-STRUCK CAPITAL Q1 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 DOUBLE-STRUCK CAPITAL Q2/DOUBLE-STRUCK CAPITAL Q1 system, our ultimate motivation is to apply algebraic multigrid within solvers for DOUBLE-STRUCK CAPITAL Q2/DOUBLE-STRUCK CAPITAL Q1 systems via the DOUBLE-STRUCK CAPITAL Q1isoDOUBLE-STRUCK CAPITAL Q2/DOUBLE-STRUCK CAPITAL Q1 discretization, which will be considered in a companion paper. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1002/nla.2426 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS |
Keywords | DocType | Volume |
additive Vanka, Braess-Sarazin, local Fourier analysis, monolithic multigrid, Stokes equations | Journal | 29 |
Issue | ISSN | Citations |
3 | 1070-5325 | 0 |
PageRank | References | Authors |
0.34 | 0 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexey Voronin | 1 | 0 | 0.34 |
| Yunhui He | 2 | 0 | 0.34 |
| Scott MacLachlan | 3 | 0 | 0.34 |
| Luke Olson | 4 | 235 | 21.93 |
| Ray Tuminaro | 5 | 0 | 0.34 |