Exa-Dune - Flexible PDE Solvers, Numerical Methods and Applications. In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project was to add flexible, application-oriented resilience capabilities into the framework. Continuous improvement of the underlying hardware-oriented numerical methods have included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin discretisations as well as partially matrix-free preconditioners. On top of that, additional scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we have focused on the adaptive choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some of the concepts are applied in a land-surface model including subsurface flow and surface runoff.

References in zbMATH (referenced in 8 articles )

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  1. Fehn, Niklas; Munch, Peter; Wall, Wolfgang A.; Kronbichler, Martin: Hybrid multigrid methods for high-order discontinuous Galerkin discretizations (2020)
  2. Moxey, David; Amici, Roman; Kirby, Mike: Efficient matrix-free high-order finite element evaluation for simplicial elements (2020)
  3. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  4. Kronbichler, Martin; Wall, Wolfgang A.: A performance comparison of continuous and discontinuous Galerkin methods with fast multigrid solvers (2018)
  5. Bauer, S.; Mohr, M.; Rüde, U.; Weismüller, J.; Wittmann, M.; Wohlmuth, B.: A two-scale approach for efficient on-the-fly operator assembly in massively parallel high performance multigrid codes (2017)
  6. Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin: A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow (2017)
  7. Mohring, Jan; Milk, René; Ngo, Adrian; Klein, Ole; Iliev, Oleg; Ohlberger, Mario; Bastian, Peter: Uncertainty quantification for porous media flow using multilevel Monte Carlo (2015)
  8. Bastian, Peter; Engwer, Christian; Göddeke, Dominik; Iliev, Oleg; Ippisch, Olaf; Ohlberger, Mario; Turek, Stefan; Fahlke, Jorrit; Kaulmann, Sven; Müthing, Steffen; Ribbrock, Dirk: EXA-DUNE: Flexible PDE solvers, numerical methods and applications (2014) ioport