A New Matrix-free Approach for Large-scale Geodynamic Simulations and its Performance

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 O(10^{12}) degrees of freedom for a global mesh resolution of 1.7 km.

@inproceedings{id2386,
  author = {Bauer, S. and Huber, M. and Mohr, M. and R\"ude, U. and Wohlmuth, B.},
  booktitle = {Computational Science - ICCS 2018},
  doi = {10.1007/978-3-319-93701-4\_2},
  editor = {Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V., Lees, M., Dongarra, J. and Sloot, P.},
  language = {en},
  pages = {17-30},
  publisher = {Springer},
  series = {Lecture Notes in Computer Science},
  title = {A New Matrix-free Approach for Large-scale Geodynamic Simulations and its Performance},
  volume = {10861},
  year = {2018},
}

%O Conference Proceedings
%A Bauer, S.
%A Huber, M.
%A Mohr, M.
%A Rüde, U.
%A Wohlmuth, B.
%B Computational Science - ICCS 2018
%R 10.1007/978-3-319-93701-4_2
%E Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V., Lees, M., Dongarra, J. and Sloot, P.
%G en
%P 17-30
%I Springer
%S Lecture Notes in Computer Science
%T A New Matrix-free Approach for Large-scale Geodynamic Simulations and its Performance
%V 10861
%D 2018