首页|Low‐order preconditioning of the Stokes equations
Low‐order preconditioning of the Stokes equations
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Wiley
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 ?1iso?2/?1 discretization of the Stokes operator as a preconditioner for the ?2/?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 ?2/?1 system, our ultimate motivation is to apply algebraic multigrid within solvers for ?2/?1 systems via the ?1iso?2/?1 discretization, which will be considered in a companion paper.
NSTL
Wiley
