By Dr. Florian Wechsung. Universidad de Nueva York
Seminar Date: 2022-02-24
We consider finite element approximations of the stationary incompressible Navier-Stokes equations. An ideal preconditioner for the linear systems arising from these equations yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. It has proven challenging to develop solvers that exhibit both properties; matrix factorisations are robust to Reynolds number but scale badly with dof count, whereas Schur complement based algorithms such as PCD and LSC scale linearly in the dof count but their performance decreases as the Reynolds number is increased. In this talk we present augmented Lagrangian based preconditioners with linear complexity and iteration counts that only grow mildly with respect to the Reynolds number. The key ingredient for this preconditioner is a tailored multigrid scheme consisting of custom smoothing and prolongation operators.