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Advances Concerning Multiscale Methods and Uncertainty Quantification in EXA-DUNE

  • Peter Bastian
  • Christian Engwer
  • Jorrit Fahlke
  • Markus Geveler
  • Dominik Göddeke
  • Oleg Iliev
  • Olaf Ippisch
  • René Milk
  • Jan Mohring
  • Steffen Müthing
  • Mario Ohlberger
  • Dirk Ribbrock
  • Stefan Turek
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 113)

Abstract

In this contribution we present advances concerning efficient parallel multiscale methods and uncertainty quantification that have been obtained in the frame of the DFG priority program 1648 Software for Exascale Computing (SPPEXA) within the funded project Exa-Dune. This project aims at the development of flexible but nevertheless hardware-specific software components and scalable high-level algorithms for the solution of partial differential equations based on the DUNE platform. While the development of hardware-based concepts and software components is detailed in the companion paper (Bastian et al., Hardware-based efficiency advances in the Exa-Dune project. In: Proceedings of the SPPEXA Symposium 2016, Munich, 25–27 Jan 2016), we focus here on the development of scalable multiscale methods in the context of uncertainty quantification. Such problems add additional layers of coarse grained parallelism, as the underlying problems require the solution of many local or global partial differential equations in parallel that are only weakly coupled.

Keywords

Uncertainty Quantification Multiscale Method Aggregate Quantity Piecewise Polynomial Function Variational Multiscale Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was funded by the DFG SPP 1648 ‘Software for Exascale Computing’ under contracts IL 55/2-1, and OH 98/5-1. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de). We also gratefully acknowledge compute time provided by the RRZK Cologne, with funding from the DFG, on the CHEOPS HPC system under project name “Scalable, Hybrid-Parallel Multiscale Methods using DUNE”.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Bastian
    • 1
  • Christian Engwer
    • 2
  • Jorrit Fahlke
    • 2
  • Markus Geveler
    • 4
  • Dominik Göddeke
    • 3
  • Oleg Iliev
    • 5
  • Olaf Ippisch
    • 6
  • René Milk
    • 2
  • Jan Mohring
    • 5
  • Steffen Müthing
    • 1
  • Mario Ohlberger
    • 2
  • Dirk Ribbrock
    • 4
  • Stefan Turek
    • 4
  1. 1.Interdisciplinary Center for Scientific ComputingHeidelberg UniversityHeidelbergGermany
  2. 2.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
  3. 3.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  4. 4.Institute of Applied MathematicsDortmundGermany
  5. 5.Fraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  6. 6.Institut für Mathematik, TU Clausthal-ZellerfeldClausthal-ZellerfeldGermany

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