Large-scale Simulation of Mantle Convection Based on a New Matrix-Free Approach

In this paper, we report on a two-scale approach for efficient matrix-free finite element simulations. It is an extended version of our previous conference publication \citeBauer:2018:IHPCES. 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, on up to 47,250 compute cores, a parallel efficiency of 93% for application of the discrete operator and 83% for a complete Uzawa V-cycle including the coarse grid solve. Our largest simulation uses a trillion O(10^12) degrees of freedom for a global mesh resolution of 1.5 km. Applicability of our new approach for geodynamical problems is demonstrated by investigating dynamic topography for classical benchmark settings as well as for high-resolution models with lateral viscosity variations.

@article{id2420,
  author = {Bauer, S. and Huber, M. and Ghelichkhan, S. and Mohr, M. and R\"ude, U. and Wohlmuth, B.},
  doi = {10.1016/j.jocs.2018.12.006},
  journal = {Journal of Computational Science},
  language = {en},
  pages = {60-76},
  title = {Large-scale Simulation of Mantle Convection Based on a New Matrix-Free Approach},
  url = {https://www.sciencedirect.com/science/article/pii/S1877750318309840?via\%3Dihub},
  volume = {31},
  year = {2019},
}

%O Journal Article
%A Bauer, S.
%A Huber, M.
%A Ghelichkhan, S.
%A Mohr, M.
%A Rüde, U.
%A Wohlmuth, B.
%R 10.1016/j.jocs.2018.12.006
%J Journal of Computational Science
%G en
%P 60-76
%T Large-scale Simulation of Mantle Convection Based on a New Matrix-Free Approach
%U https://www.sciencedirect.com/science/article/pii/S1877750318309840?via%3Dihub
%V 31
%D 2019