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

Bauer, S., M. Huber, M. Mohr, U. Rüde, and B. Wohlmuth (2018), A New Matrix-free Approach for Large-scale Geodynamic Simulations and its Performance, in Computational Science - ICCS 2018, Lecture Notes in Computer Science, vol. 10861, edited by Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V., Lees, M., Dongarra, J. and Sloot, P., pp. 17-30, Springer, doi:10.1007/978-3-319-93701-4_2.

Abstract
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.
BibTeX
@inproceedings{id2386,
  author = {S. Bauer and M. Huber and M. Mohr and U. R{\"u}de and B. Wohlmuth},
  booktitle = {Computational Science - ICCS 2018},
  editor = {Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V., Lees, M., Dongarra, J. and Sloot, P.},
  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},
  doi = {10.1007/978-3-319-93701-4{\_}2},
}
EndNote
%A Bauer, S.
%A Huber, M.
%A Mohr, M.
%A Rüde, U.
%A Wohlmuth, B.
%E Shi, Y., Fu, H., Tian, Y., Krzhizhanovskaya, V., Lees, M., Dongarra, J. and Sloot, P.
%D 2018
%V 10861
%P 17-30
%T A New Matrix-free Approach for Large-scale Geodynamic Simulations and its Performance
%B Computational Science - ICCS 2018
%I Springer
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Printed 06. Dec 2019 01:28