An assessment of solvers for saddle point problems emerging from the incompressible Navier--Stokes equations
- Ahmed, Naveed
- Bartsch, Clemens
- John, Volker
- Wilbrandt, Ulrich
2010 Mathematics Subject Classification
- Linear saddle point problems, inf-sup stable pairs of finite element spaces, UMFPACK, flexible GMRES, coupled multigrid preconditioners with Vanka smoother, Least Squares Commutator preconditioners
Efficient incompressible flow simulations, using inf-sup stable pairs of finite element spaces, require the application of efficient solvers for the arising linear saddle point problems. This paper presents an assessment of different solvers: the sparse direct solver UMFPACK, the flexible GMRES (FGMRES) method with different coupled multigrid preconditioners, and FGMRES with Least Squares Commutator (LSC) preconditioners. The assessment is performed for steady-state and time-dependent flows around cylinders in 2d and 3d. Several pairs of inf-sup stable finite element spaces with second order velocity and first order pressure are used. It turns out that for the steady-state problems often FGMRES with an appropriate multigrid preconditioner was the most efficient method on finer grids. For the time-dependent problems, FGMRES with LSC preconditioners that use an inexact iterative solution of the velocity subproblem worked best for smaller time steps.
- Comput. Methods Appl. Mech. Engrg., 331 (2018), pp. 492--513, DOI 10.1016/j.cma.2017.12.004 .