A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

Abstract

We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O1012)) degrees of freedom for a global mesh resolution of 1.7 km.