Low-order preconditioning of the Stokes equations
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Univ. of Waterloo, ON (Canada)
- Memorial Univ. of Newfoundland, Newfoundland and Labrador (Canada)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
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 Q1 iso Q2/Q1 discretization of the Stokes operator as a preconditioner for the Q2/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. Furthermore, these results are then verified and compared against the measured multigrid performance. While geometric multigrid can be applied directly to the Q2/Q1 system, our ultimate motivation is to apply algebraic multigrid within solvers for Q2/Q1 systems via the Q1 iso Q2/Q1 discretization, which will be considered in a companion paper.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- NA0003525
- OSTI ID:
- 1834325
- Alternate ID(s):
- OSTI ID: 1833908
- Report Number(s):
- SAND-2021-14411J; 701513
- Journal Information:
- Numerical Linear Algebra with Applications, Vol. 29, Issue 3; ISSN 1070-5325
- Publisher:
- WileyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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