Robust multigrid techniques for augmented Lagrangian preconditioning of incompressible Stokes equations with extreme viscosity variations

by   Yu-hsuan Shih, et al.

We present augmented Lagrangian Schur complement preconditioners and robust multigrid methods for incompressible Stokes problems with extreme viscosity variations. Such Stokes systems arise, for instance, upon linearization of nonlinear viscous flow problems, and they can have severely inhomogeneous and anisotropic coefficients. Using an augmented Lagrangian formulation for the incompressibility constraint makes the Schur complement easier to approximate, but results in a nearly singular (1,1)-block in the Stokes system. We present eigenvalue estimates for the quality of the Schur complement approximation. To cope with the near-singularity of the (1,1)-block, we extend a multigrid scheme with a discretization-dependent smoother and transfer operators from triangular/tetrahedral to the quadrilateral/hexahedral finite element discretizations [ℚ_k]^d×ℙ_k-1^disc, k≥ 2, d=2,3. Using numerical examples with scalar and with anisotropic fourth-order tensor viscosity arising from linearization of a viscoplastic constitutive relation, we confirm the robustness of the multigrid scheme and the overall efficiency of the solver. We present scalability results using up to 28,672 parallel tasks for problems with up to 1.6 billion unknowns and a viscosity contrast up to ten orders of magnitude.


Parameter-free preconditioning for nearly-incompressible linear elasticity

It is well known that via the augmented Lagrangian method, one can solve...

A Mass Conserving Mixed hp-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning

This is the third part in a series on a mass conserving, high order, mix...

hp-Multigrid preconditioner for a divergence-conforming HDG scheme for the incompressible flow problems

In this study, we present an hp-multigrid preconditioner for a divergenc...

Preconditioners for computing multiple solutions in three-dimensional fluid topology optimization

Topology optimization problems generally support multiple local minima, ...

Please sign up or login with your details

Forgot password? Click here to reset