Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE

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, 2527 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.