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

偏微分方程（PDEs）作为数学模型被广泛应用于自然科学、工程学，最近也被应用于生物医学、社会科学以及金融领域。因此，它们的数值解对于理解、精确模拟和优化自然、人类和工程系统具有重要意义。在许多应用中，有限元方法（FEM）是将PDE转换为有限维的、可计算解决的问题的首选方法。这笔交易。II项目是一个开源的FEM软件库，它使科学家能够解决许多学科的pde，通过提供工具来解决基本上适用于FEM的所有pde，它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，将增加新的功能，并扩展用户和贡献者社区，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。该项目将进一步支持其用户和开发人员社区，通过专门承担志愿者无法承担的工作，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，将处理以下四个类别中的以下工作项：基础特性太大或太复杂，志愿者无法解决：该团队将研究并实施有效和可扩展的方法，以支持并行、自适应多网格和hp FEM。2. 通过更多的教程计划和youtube视频讲座来扩展文档和培训模块：这将进一步扩大项目的范围，并扩展计算科学社区的教育。3. 持续集成和封装基础设施，以更好地支持开发步伐。4. 支持和扩大交易。通过暑期学校、研讨会、黑客马拉松和对新来者的悉心指导，II的社区蓬勃发展。该奖项反映了美国国家科学基金会的法定使命，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.