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

偏微分方程(PDE)在自然科学、工程学以及最近在生物医学和社会科学以及金融学中被用作数学模型。因此，它们的数值解对于理解、准确模拟和优化自然、人类和工程系统具有重要意义。在许多应用中，有限元方法是将偏微分方程组转化为有限维可计算可解问题的选择方法。Deal II项目是一个开源的有限元软件库，使科学家能够解决许多学科的偏微分方程组，通过提供工具来求解基本上所有适合于有限元的偏微分方程组，从而支持在科学和工程的几乎所有部分进行模拟和计算发现。在这个项目中，将增加新的功能，并扩大用户和贡献者社区，以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人员社区的项目。该项目将进一步加强其用户和开发人员社区，专门从事志愿人员不能期望的工作，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，将处理以下四类工作项目：1.基础特征太大或太复杂，志愿者无法解决：该团队将研究和实施高效和可扩展的方法，以支持并行、自适应多重网格和惠普有限元。2.通过更多的教程计划和YouTube主持的视频讲座扩展文件和培训模块：这将进一步扩大该项目的覆盖范围，并扩大对计算科学界的教育。3.持续整合和包装基础设施，更好地支撑发展步伐。4.支持和扩大交易。II通过暑期学校、研讨会、黑客马拉松和对新来者的仔细指导来支持蓬勃发展的社区。这个奖项反映了NSF的法定使命，通过使用基金会的智力优势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.