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

在这个由来自开源项目Dune和Fest的计算机科学家、数学家和领域专家组成的跨学科项目中，我们开发、分析、实施和优化了新的数值算法和软件，用于在未来的亿级系统上可伸缩地求解偏微分方程组(PDE)，展示了一个异质的大规模并行体系结构。Dune软件框架通过使用最先进的编程技术和符合公共接口的可互换组件，将灵活性和通用性与高效率结合在一起。将FEAST项目的面向硬件的数值技术结合到这些组件中，使我们在第一个资助阶段就可以优化利用具有三级并行(SIMD矢量化、多线程、消息传递)的异类体系结构的性能，同时能够支持稳步增长的Dune用户社区的各种不同应用。为了应对硬件故障概率的增加，第二个资助阶段的一个中心目标是增加灵活性，将面向应用的恢复能力纳入框架，该框架基于公共基础设施，一方面包括随时可用的自我稳定迭代求解器，另一方面包括全局和局部检查点重启技术。通过将基于无矩阵和分解的高阶间断Galerkin离散化和基于矩阵的代数多重网格低阶子空间修正格式相结合，实现了面向硬件的数值方法的不断改进，从而获得了稳健和高性能的求解结果。最重要的是，通过利用多尺度和不确定性量化方法提供的大规模粗粒度并行性，极大地促进了可伸缩性，其中我们现在专注于粗/细尺度和重叠区域的自适应选择，以及局部缩减基多尺度方法和多层蒙特卡罗算法的组合。作为该项目的一个组成部分，我们建议将我们的可伸缩PDE解算器组件整合到下一代陆面模型中，包括地下水流、植被、蒸发和地表径流。这项开发是与哈勒的Helmholtz环境研究中心(UFZ)密切合作进行的，该中心提供额外的建模专业知识以及来自多个来源(试验点、地球物理数据、遥感、DOTS)的测量数据。我们共同致力于为环境研究界提供一个开源工具，有助于解决具有高度社会相关性的问题。

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.