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

Beitrag bei einer Tagung

Details zur Publikation

Autor(en): Bartuschat D, Rüde U, Thoennes D, Kohl N, Drzisga DP, Huber M, John L, Waluga C, Wohlmuth BI, Bauer S, Mohr M, Bunge HP
Jahr der Veröffentlichung: 2017
Sprache: Englisch


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 10^{12} km^3 and many time steps.

These simulations are only possible with highly efficient codes that exhbit 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,

modeling 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.

HHG combines the flexibility of unstructured tetrahedral meshes with the efficiency of structured grids for finite element discretizations.

The design of this framework 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 ($10^13$) unknowns

on Peta-Scale systems using compute times of a few minutes.

FAU-Autoren / FAU-Herausgeber

Bartuschat, Dominik Dr.-Ing.
Lehrstuhl für Informatik 10 (Systemsimulation)
Bauer, Simon
Lehrstuhl für Informatik 10 (Systemsimulation)
Drzisga, Daniel Peter
Lehrstuhl für Informatik 10 (Systemsimulation)
Huber, Markus
Lehrstuhl für Informatik 10 (Systemsimulation)
Kohl, Nils
Lehrstuhl für Informatik 10 (Systemsimulation)
Rüde, Ulrich Prof. Dr.
Lehrstuhl für Informatik 10 (Systemsimulation)
Thoennes, Dominik
Lehrstuhl für Informatik 10 (Systemsimulation)

Autor(en) der externen Einrichtung(en)
Ludwig-Maximilians-Universität (LMU)
Technische Universität München (TUM)


Bartuschat, D., Rüde, U., Thoennes, D., Kohl, N., Drzisga, D.P., Huber, M.,... Bunge, H.-P. (2017). A parallel finite element multigrid framework for geodynamic simulations with more than ten trillion unknowns. Oslo, Norwegen.

Bartuschat, Dominik, et al. "A parallel finite element multigrid framework for geodynamic simulations with more than ten trillion unknowns." Proceedings of the CSEConf2017 -- 2017 International Conference on Computational Science and Engineering - Software, Education, and Biomedical applications, Oslo, Norwegen 2017.


Zuletzt aktualisiert 2018-30-07 um 13:30