Collaborative Research: Frameworks: Software: Future Proofing the Finite Element Library Deal.II -- Development and Community Building

偏微分方程（PDE）被用作整个自然科学，工程，以及最近在生物医学和社会科学以及金融中的数学模型。因此，它们的数值解在理解、准确模拟和优化自然、人类和工程系统方面具有重要意义。在许多应用中，有限元方法（FEM）是将PDE转换成有限维、计算可解问题的选择方法。Deal.II项目是一个开源FEM软件库，使科学家能够解决许多学科的偏微分方程，通过提供工具来解决基本上所有适用于FEM的偏微分方程，支持几乎所有科学和工程领域的模拟和计算发现。在这个项目中，新的功能将被添加，用户和贡献者社区将被扩展到包括更多的科学领域。Deal.II是一个拥有蓬勃发展的全球用户和开发者社区的项目。该项目将进一步促进其用户和开发人员社区，具体开展志愿人员无法完成的工作，或加强项目长期独立可持续性所必需的工作。根据最近的用户调查，将解决以下四个类别中的以下工作项目：1。基础功能太大或太复杂，志愿者无法解决：该团队将研究和实施有效和可扩展的方法，以支持并行，自适应多重网格和hp FEM。2.通过更多的教程计划和YouTube托管的视频讲座扩展文档和培训模块：这将进一步扩大项目的覆盖范围，并扩展计算科学社区的教育。3.持续集成和打包基础设施，以更好地支持开发速度。4.通过暑期学校、研讨会、黑客马拉松和对新来者的精心指导来支持和扩大Deal.II蓬勃发展的社区。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Partial differential equations (PDEs) are used as mathematical models throughout the natural sciences, engineering, and more recently also in the biomedical and social sciences as well as in finance. Their numerical solution is, consequently, of great relevance in understanding, accurately simulating, and optimizing natural, human, and engineered systems. In many applications, finite element methods (FEM) are the method of choice converting the PDE into finite dimensional, computationally solvable problems. The deal.II project is an open source FEM software library that enables scientists to solve PDEs across many disciplines, that supports simulation and computational discovery in virtually all parts of the sciences and engineering by providing tools to solve essentially all PDEs amenable to the FEM. In this project new capabilities will be added and the user and contributor community expanded to include additional science domains.Deal.II is a project with a thriving, world-wide user and developer community. This project will further enable its community of users and developers, by undertaking specifically for work that can either not be expected of volunteers, or that is necessary to strengthen the long-term independent sustainability of the project. Based on a recent user survey, the following work items in the following four categories will be addressed: 1. Foundational features too large or complicated to be tackled by volunteers: the team will research and implement efficient and scalable approaches to support parallel, adaptive multigrid and hp FEM. 2. Expand documentation and training modules through more tutorial programs and YouTube-hosted video lectures: This will further broaden the reach of the project and extend the education for the computational science community. 3. Continuous integration and packaging infrastructure to better support the pace of development. 4. Support and expand deal.II's thriving communities through a summer school, workshops, hackathons, and careful mentoring of newcomers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.