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

在这个由计算机科学家、数学家和来自开源项目DUNE和FEAST的领域专家组成的跨学科项目中，我们开发、分析、实现和优化新的数值算法和软件，用于在未来的百亿亿级系统上展示异构大规模并行架构的偏微分方程（PDEs）的可扩展解决方案。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整合到这些组件中，使我们在第一个资助阶段就可以利用异构架构的三层并行性（SIMD向量化、多线程、消息传递）来优化其性能，同时能够支持来自稳步增长的DUNE用户社区的各种不同应用程序。为了应对硬件故障增加的可能性，第二个资助期的中心目标是在框架中添加灵活的、面向应用的恢复能力，该框架基于通用基础设施，一方面包括随时可用的自稳定迭代求解器，另一方面包括全局和本地检查点重启技术。通过将基于无矩阵和分解的高阶不连续伽辽金离散与基于矩阵的代数多网格低阶子空间校正方案相结合，实现了底层面向硬件的数值方法的不断改进，从而获得了鲁棒性和高性能的求解器。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量粗粒度并行性，实现了极大的可扩展性，我们现在关注的是粗/细尺度和重叠区域的自适应选择，以及局部降基多尺度方法和多层蒙特卡罗算法的结合。作为项目的一个组成部分，我们建议将可扩展的PDE求解器组件整合到下一代陆地表面模型中，包括地下流、植被、蒸发和地表径流。这一发展是与哈勒的亥姆霍兹环境研究中心（UFZ）密切合作进行的，该中心提供了额外的建模专业知识以及来自多个来源（实验地点、地球物理数据、遥感、点）的测量数据。我们一起着手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.