As one of the grand research questions of the 21st century the understanding of the Earth's interior requires highly resolved models of mantle circulation. With a targeted global resolution to length scales of 1 km finite element discretizations lead to linear systems with trillions (10¹2) of unknowns. This talk presents the concept of Hybrid Tetrahedral Grids as an approach to design massively parallel algorithms and data structures that enable the efficient solution of such problems at the extreme-scale. A strong focus is put on matrix-free geometric multigrid methods for the approximation of the Stokes system that demonstrate scalability to more than three trillion (3 x 10¹2) unknowns on about 150, 000 parallel processes.
Nils Kohl (Tue,) studied this question.