Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications

TL;DR

The Exa-Dune project develops scalable, resilient numerical algorithms and software for solving PDEs on future exascale heterogeneous systems, incorporating advanced methods, parallelism, and applications in land-surface modeling.

Contribution

It introduces flexible, application-oriented resilience features and advanced numerical techniques optimized for exascale architectures, including GPU acceleration and multiscale methods.

Findings

Enhanced scalability through coarse grained parallelism

Implementation of GPU-based sparse approximate inverses

Application of methods in land-surface modeling

Abstract

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.