# Christian Helanow: Block preconditioning the p-Stokes equations in ice-sheet models

**Time: **
Thu 2022-03-31 14.00 - 15.00

**Location: **
KTH, Seminar room 3721, Lindstedsvägen 25

**Participating: **
Christian Helanow (Stockholm University)

**Abstract: **The deformation of ice can accurately be modeled as non-linear Stokes flow. The constitutive equation for ice, relating strain rates to stresses, is that of a singular power law which when discretizing the system of equations gives rise to a poorly conditioned linear system. The system is of saddle-point nature and its character depends on e.g. the effective viscosity and chosen regularization parameter. This motivates the use of block preconditioners that explicitly take into account the properties of the underlying problem. In the context of ice-sheet modeling using the p-Stokes equations block preconditioners have been used and numerically investigated with a heuristic motivation. However, in more general non-Newtonian settings, with focus on Bingham fluids, bounds on the eigenvalues for the block-preconditioned Schur complement have been derived. We attempt to adapt the theory of these studies to include Schur-complement preconditioners for singular power-law fluids, and numerically investigate how the proposed block preconditioner is affected by the specifics of ice-sheet simulations.