A parallel finite element multigrid framework for geodynamic simulations with more than ten trillion unknowns

Time: 14:00-14:20 Numerical simulations are an indispensable tool in geosciences for understanding geodynamic processes inside the Earth. Due to the enormous spatial and time scales and the inaccessibility of the Earth's... [ view full abstract ]

Time: 14:00-14:20

Numerical simulations are an indispensable tool in geosciences for understanding geodynamic processes inside the Earth. Due to the enormous spatial and time scales and the inaccessibility of the Earth's interior to direct measurements, studying these processes requires a combination of sophisticated computer simulations and mostly indirect observations.
Heating inside the Earth's core and mantle causes convection currents in the solid Earth mantle, which results in a viscous flow on geological time scales of millions of years. This mantle convection is the driving mechanism of plate tectonics, which causes mountain building, earthquakes and volcanism. However, many details of the physical processes in Earth mantle convection are poorly known, such as appropriate rheological parameters or the mantle viscosity structure.
To allow for the use of realistic physical parameters, Earth mantle convection simulations require extremely large grids for a sufficient resolution of the mantle volume of 10¹² km³ and many time steps. These simulations are only possible with highly efficient codes that exhibit excellent parallel scalability on modern supercomputers. In this talk, we present a framework for such large-scale time-dependent mantle convection simulations on a thick spherical shell with variable viscosity.
In the simulations a nonlinear coupled multiphysics problem of Stokes equation coupled to the energy equation is solved, modelling the conservation of momentum, mass, and energy. These equations are discretized with finite elements and the solution is computed in the Hierarchical Hybrid Grids (HHG) framework.
This framework combines the flexibility of unstructured tetrahedral meshes with the efficiency of structured grids for finite element discretizations.
The design of HHG is motivated by the challenging goal of achieving high performance on large-scale and parallel finite element simulations on supercomputers. HHG exploits the performance and efficiency of nested structured grid hierarchies and hierarchically organized data structures combined with the flexibility of unstructured grids. To this end, HHG combines grid partitioning and regular refinement in such a way that an execution paradigm using stencils can be realized. Within uniform blocks of the mesh three-dimensional stencils are applied in the fashion of a finite difference method.
We present transient simulation results of the temperature distribution for the coupled flow and transport problem, as well as the stationary flow field for variable temperature-dependent viscosity with high viscosity contrasts.
Moreover, scaling results are presented to show that our approach facilitates solving systems in excess of ten trillion (10¹³) unknowns on Peta-Scale systems using compute times of a few minutes.