Massively Parallel Large Scale Stokes Flow Simulation

In many applications, physical models consisting of a Stokes-type equation that is coupled to a convection-dominated transport equation play an important role, e.g., in mantle-convection or ice-sheet dynamics. In the iterative treatment of such problems the computational cost is usually dominated by the solution procedure for the Stokes part. Hence, we focus on massively scalable and fast multigrid solvers for the arising saddle point problem. To gain deeper insight into the performance characteristics, we evaluate the multigrid efficiency systematically and address the methodology of algorithmic resilience. Three methods based on the HHG software framework will be presented and are shown to solve FE systems with half a billion unknowns even on standard workstations. On petascale systems they furthermore exhibit excellent scalability.This together with the optimised performance on each node leads to superior supercomputing efficiency. Indefinite systems with up to ten trillion (10^13) unknowns can be solved in less than13 minutes compute time