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

偏微分方程式作为数学模型被广泛应用。因此，它们的数值解对于精确模拟和优化科学、工程和其他领域的过程至关重要。在过去的十年中，出现了支持此类应用的大型且成功的库。虽然这些库提供了小规模计算所需的大部分此类代码，但许多现实应用程序产生了数亿或数十亿未知的问题，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，限制了计算科学专家对许多大型公共支持计算设施的访问，包括来自许多领域的科学家，对他们来说，计算模拟将是一个有用的工具。该项目旨在构建软件基础设施，以允许广泛领域的科学家利用这些大量资源。该项目旨在以通用的方式支持在大规模并行计算资源上大规模求解偏微分方程组的软件基础设施。它将建立在科学计算中最成功的两个库--有限元库Deal.II和为前者提供并行线性代数能力的Trilinos上。具体地说，我们将：(I)支持交易中普遍存在的大规模并行计算；(Ii)研究和开发对两个库中都有数十亿个未知数的问题的无缝支持，并改善两者之间的交互；(Iii)在今天的集群上利用节点内的并行性；(Iv)通过实现两个真实世界的应用程序来确保我们工作的广泛适用性。Deal.II和Trilinos都拥有庞大、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、定期授课课程、邮件列表和重点项目中的直接联系，积极吸引这些社区的参与。

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.