Collaborative Research: SI2-SSI: Open Source Support for Massively Parallel, Generic Finite Element Methods

偏微分方程作为数学模型被广泛应用。因此，它们的数值解对于科学、工程和其他领域的过程的精确模拟和优化至关重要。在过去的十年中，出现了支持此类应用程序的大型且成功的库。虽然这些库提供了此类代码用于小规模计算所需的大部分内容，但许多实际应用会产生数亿或数十亿未知数的问题，并需要具有数千个处理器核心的集群，但目前对此类问题的通用支持很少。限制对许多大型公共支持的计算设施的访问，只允许计算科学领域的专家使用，并将计算模拟将是有用工具的许多领域的科学家排除在外。这个项目打算建立软件基础设施，允许广泛的科学家利用这些巨大的资源。本项目旨在以通用的方式支持大规模并行计算资源上的偏微分方程大规模解的软件基础设施。它将建立在两个最成功的科学计算库——有限元库的基础上。为前者提供并行线性代数能力的Trilinos。具体来说，我们将：(i)在deal.II中普遍支持大规模并行计算；（ii）研究和开发对两个图书馆中数十亿未知问题的无缝支持，并改善两者之间的互动；（iii）利用当前集群的节点内并行性；（iv）通过实施两项实际应用，确保我们的工作在广泛的基础上适用。这两个协议。II和Trilinos拥有庞大、活跃和多样化的开发人员和用户社区，该项目将通过用户会议、短期课程、定期授课、邮件列表和重点项目的直接联系等方式积极参与这些社区。

Partial differential equations are used in a wide variety of applications asmathematical models. Their numerical solution is, consequently, of primeimportance for the accurate simulation and optimization of processes in thesciences, engineering, and beyond.The last decade saw the emergence of large and successful libraries thatsupport such applications. While these libraries provide most of what suchcodes need for small-scale computations, many realistic applications yieldproblems of hundreds of millions or billions of unknowns and require clusterswith thousands of processor cores, but there is currently little genericsupport for such problems, limiting access to the many large publiclysupported computing facilities to experts in computational science andexcluding scientists from many fields for whom computational simulation wouldbe a useful tool. This project intends to build the software infrastructure that will allow awide cross section of scientists to utilize these large resources.This project intends to support the software infrastructure for thelarge-scale solution of partial differential equations on massively parallelcomputational resources in a generic way. It will build on two of the mostsuccessful libraries for scientific computing, the finite element librarydeal.II, and Trilinos that provides the parallel linear algebra capabilitiesfor the former. Specifically, we will: (i) Make support for massively parallelcomputations ubiquitous in deal.II; (ii) Research and develop seamless supportfor problems with billions of unknowns in both libraries and improve theinteraction between the two; (iii) Exploit intra-node parallelism on today'sclusters; (iv) Ensure the applicability of our work on a broad basis byimplementing two real-world applications. Both deal.II and Trilinos have large, active and diverse developer and usercommunities, and this project will actively engage these communities throughuser meetings, short courses, regularly taught classes, mailing lists, anddirect contact in focused projects.