EXA-DUNE - Flexible PDE Solvers, Numerical Methods, and Applications

• Applicants: Professor Dr. Peter Bastian; Professor Dr. Christian Engwer; Professor Dr. Dominik Göddeke; Professor Dr. Oleg Iliev; Professor Dr. Olaf Ippisch; Professor Dr. Mario Ohlberger; Professor Dr. Stefan Turek
• Subject Area: Mathematics
• Term: from 2012 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 230658507

In this interdisciplinary project consisting of computer scientists, mathematicians and domain experts from the open source projects DUNE and FEAST we develop, analyse, implement and optimise new numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. The DUNE software framework combines flexibility and generality with high efficiency by the use of state-of-the-art programming techniques and interchangeable components conforming to a common interface.Incorporating the hardware-oriented numerical techniques of the FEAST project into these components allows us already during the first funding phase to optimally exploit the performance of heterogeneous architectures with their three-level parallelism (SIMD vectorisation, multithreading, message passing) while at the same time being able to support a variety of different applications from the steadily growing DUNE user community.In order to cope with the increased probability of hardware failures, a central aim in the second funding period is to add flexible, application-orientied resilience capabilities into the framework which, based on a common infrastructure, includes on the one hand ready-to-use self-stabilising iterative solvers and on the other hand global and local checkpoint restart techniques. Continuous improvement of the underlying hardware-oriented numerical methods is achieved by combining matrix-free sum-factorisation based high-order discontinuous Galerkin discretisations with matrix-based algebraic multigrid low-order subspace correction schemes resulting in both robust and performant solvers. On top of that, extreme scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we now focus 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. As an integral part of the project we propose to bring together our scalable PDE solver components in a next-generation land-surface model including subsurface flow, vegetation, evaporation and surface runoff. This development is carried out in close cooperation with the Helmholtz-Centre for environmental research (UFZ) in Halle which provides the additional modelling expertise as well as measurement data from multiple sources (experimental sites, geophysical data, remote sensing, \dots). Together we set out to provide the environmental research community with an open source tool that contributes to the solution of problems with high social relevance.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1648: Software for Exascale Computing