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

协作研究：框架：软件：面向未来的有限元库交易.II——开发和社区建设

• 批准号: 1835673
• 负责人: Wolfgang Bangerth
• 金额: $ 100万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1835673&HistoricalAwards=false
• 关键词: Collaborative; Research; Frameworks; Software; Future

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.

部分微分方程（PDE）用作自然科学，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，它们的数值解决方案在理解，准确模拟和优化自然，人类和工程系统方面具有很大的意义。在许多应用中，有限元方法（FEM）是选择将PDE转换为有限维度，计算解决方案问题的方法。 Deal.ii项目是一个开源的FEM软件库，使科学家能够解决许多学科的PDE，该PDE通过提供基本上可以求解所有可与FEM合并的所有PDE来支持科学和工程的模拟和计算发现。在此项目中，将添加新功能，并将用户和贡献者社区扩展到包括其他科学领域。Deal.ii是一个具有蓬勃发展，全球用户和开发人员社区的项目。该项目将通过专门为志愿者无法期望的工作而专门为加强项目的长期独立可持续性而进行的工作进一步使其用户和开发人员社区。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。志愿者太大或复杂而无法应对的基础功能：团队将研究和实施高效且可扩展的方法，以支持并行，适应性的Multigrid和HP FEM。 2。通过更多的教程计划和YouTube主持的视频讲座扩展文档和培训模块：这将进一步扩大项目的影响力并扩展计算科学界的教育。 3。连续集成和包装基础架构，以更好地支持开发步伐。 4。通过暑期学校，研讨会，黑客马拉松和仔细指导新移民的蓬勃发展的社区支持和扩大交易。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子评估来支持的，并具有更广泛的影响。

项目成果

Propagating Geometry Information to Finite Element Computations

• DOI: 10.1145/3468428
• 发表时间: 2019-10
• 期刊: ACM Transactions on Mathematical Software (TOMS)
• 作者: L. Heltai;W. Bangerth;M. Kronbichler;A. Mola

The deal.II library, Version 9.1

• DOI: 10.1515/jnma-2019-0064
• 发表时间: 2019-12-01
• 期刊: JOURNAL OF NUMERICAL MATHEMATICS
• 影响因子: 3
• 作者: Arndt, Daniel;Bangerth, Wolfgang;Wells, David
• 通讯作者: Wells, David

Residual-based a posteriori error estimation for hp-adaptive finite element methods for the stokes equations

斯托克斯方程 HP 自适应有限元方法的基于残差的后验误差估计

• DOI: 10.1515/jnma-2018-0047
• 发表时间: 2018
• 期刊: Journal of Numerical Mathematics
• 影响因子: 3
• 作者: Ghesmati, A.;Bangerth, W.;Turcksin, B.
• 通讯作者: Turcksin, B.

I’m stuck! How to efficiently debug computational solid mechanics models so you can enjoy the beauty of simulations

我被困住了！

• DOI: 10.1016/j.euromechsol.2022.104845
• 发表时间: 2023
• 期刊: European Journal of Mechanics - A/Solids
• 作者: Comellas, Ester;Pelteret, Jean-Paul;Bangerth, Wolfgang
• 通讯作者: Bangerth, Wolfgang

Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations

具有自适应网格细化的灵活且可扩展的细胞内粒子方法用于地球动力学计算

• DOI: 10.1029/2018gc007508
• 发表时间: 2018
• 期刊: Geosystems
• 作者: Gassmöller, Rene;Lokavarapu, Harsha;Heien, Eric;Puckett, Elbridge Gerry;Bangerth, Wolfgang
• 通讯作者: Bangerth, Wolfgang