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，实施和优化新的数值算法和软件，用于在未来的exascale系统上可扩展地解决偏微分方程（PDE），表现出异构的大规模并行架构。 DUNE软件架构采用最先进的程式设计技术和符合通用界面的可互换组件，兼具灵活性、通用性和高效率。将FEAST项目中面向硬件的数值技术融入这些组件中，使我们在第一个资助阶段就能以最佳方式利用具有三级并行性的异构架构的性能（SIMD向量化、多线程、消息传递），同时能够支持来自稳步增长的DUNE用户群体的各种不同应用。为了科普硬件故障的可能性增加，第二个资助期的中心目标是在框架中添加灵活的、以应用为导向的恢复能力，基于一个共同的基础设施，包括一方面随时可用的自稳定迭代求解器，另一方面全球和本地检查点重启技术。不断改进的底层硬件为导向的数值方法是通过结合矩阵的无和因式分解为基础的高阶不连续Galerkin离散与矩阵为基础的代数多重网格低阶子空间校正计划，从而在鲁棒性和高性能的求解器。最重要的是，极端的可扩展性是通过利用大规模的粗粒度并行提供多尺度和不确定性量化方法，我们现在专注于自适应选择的粗/细尺度和重叠区域，以及结合本地减少基础多尺度方法和多级蒙特-卡罗算法。 作为该项目的一个组成部分，我们建议将我们的可扩展PDE求解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。 这一开发是与哈雷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（实验场地，地球物理数据，遥感）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.