Firedrake: high performance, high productivity simulation for the continuum mechanics community.

Firedrake：连续介质力学界的高性能、高生产力模拟。

• 批准号: EP/W029731/1
• 负责人: David Ham
• 金额: $ 87.77万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW029731%2F1
• 关键词: Firedrake; performance; productivity; simulation; continuum

This project will extend and enhance the Firedrake automated finite elementsimulation system to allow researchers across the field of continuum mechanicsto simulate a wider range of physical phenomena using more sophisticatedtechniques than they would be able to code themselves, and to do so byspecifying the simulation from highly productive mathematical interfaceembedded in Python.The simulation of continuous physical systems described by partial differentialequations (PDEs) is a mainstay activity of computational science. This spansthe integrity of structures, the efficiency of industrial processes built onfluid flow, and the propagation of electromagnetic waves from an antenna toname but a few. Each simulation demands the choice of an appropriate PDE, an accurate andstable discretisation, the efficient parallel assembly of the resultingmatrices and vectors, and the fast, scalable solution of the resultingnumerical system. Every simulation is the composition of a chain of processes,each of which is a research domain in its own right. Most computational continuum mechanics research happens in small teams. Thesegroups constantly tackle new problems, needing changes at every level of thesimulation chain. The challenge is to allow individual researchers and smallteams to put together their own simulations, without requiring the impossibleby every researcher becoming an expert on the implementation of every stage ofthe process.Firedrake employs a mathematical language embedded in Python that enablesresearchers to write the simulation they wish to execute in a highly productiveand concise way. The high performance parallel implementation of the simulationis then automatically generated by specialised compilers at runtime. The resultis a system in which scientists and engineers write maths and get simulation.This frees researchers to focus on the continuum mechanics question at handrather than the mechanics of creating the simulation.Firedrake is a widely employed community code with hundreds of publishedapplications across continuum mechanics. For many researchers, Firedrakeclearly already meets at least some of their needs. However, the sophisticationof continuum mechanics research is boundless: there are always users andpotential users whose problems cannot fully be expressed in Firedrake's highlevel mathematical language. This project will address several suchlimitations, chosen in response to formal Firedrake user engagement over thelast two years.First, we will extend Firedrake's capabilities in solving coupled multi-domainsystems. This will enable Firedrake users to more effectively tackle simulationchallenges such as the impact of sea waves on wind turbine columns. Second, we will extend Firedrake's automated inverse capabilities to includecomplex-valued problems. This will significantly benefit users wishingto simulate optimal design problems involving electromagnetic waves.Third, we will extend the range of meshes that Firedrake can employ to includeunstructured hexahedral meshes, and hierarchically refined meshes. This willimprove Firedrake's support for efficient high order discontinuous Galerkindiscretisations and for multiscale problems such as folding of materials.In addition to extending Firedrake's technical capabilities, this project willgrow and support the community of continuum mechanics researchers usingFiredrake. We will reduce the technical knowledge needed to install Firedrakeby providing packages for the main desktop operating systems. We will runtutorials, workshops, and provide online support to new and existing Firedrakeusers. An "open door" programme of user visits to the Firedrake core developerswill provide personal one on one assistance with their simulation needs. Wewill invest significant time in the extension and maintenance of Firedrake's highquality documentation.

该项目将扩展和增强Firedrake自动有限元模拟系统，使连续介质力学领域的研究人员能够使用比他们自己编码更简单的技术来模拟更广泛的物理现象，并通过从Python中嵌入的高效数学接口指定模拟来实现。由偏微分方程（PDE）描述的连续物理系统的模拟是计算科学的一项重要活动。这包括结构的完整性，建立在流体流动上的工业过程的效率，以及天线电磁波的传播等等。每个模拟要求选择一个适当的偏微分方程，一个准确和稳定的离散化，高效的并行组装的resultingmatrix和向量，和快速，可扩展的解决方案resultingnumerical system。每个模拟都是一系列过程的组成，每个过程本身都是一个研究领域。大多数计算连续介质力学研究都是在小团队中进行的。这些小组不断地解决新问题，需要在模拟链的每一个层面上进行改变。挑战在于允许单个研究人员和小团队将他们自己的模拟放在一起，而不需要每个研究人员都成为该过程每个阶段实现的专家。Firedrake采用了嵌入在Python中的数学语言，使研究人员能够以高效和简洁的方式编写他们希望执行的模拟。高性能并行实现的simulationis然后自动生成的专用编译器在运行时。结果是一个系统，科学家和工程师在其中编写数学和得到模拟。这使研究人员能够专注于手头的连续介质力学问题，而不是创建模拟的机制。Firedrake是一个广泛使用的社区代码，在连续介质力学中有数百个已开发的应用程序。对于许多研究人员来说，Firedrakeclearly至少已经满足了他们的一些需求。然而，连续介质力学研究的解释是无限的：总有用户和潜在用户的问题不能完全表达在Firedrake的高级数学语言。这个项目将解决几个这样的限制，选择在响应正式Firedrake用户参与在过去的两年。首先，我们将扩展Firedrake的能力，解决耦合多域系统。这将使Firedrake用户能够更有效地应对模拟挑战，例如海浪对风力涡轮机柱的影响。其次，我们将扩展Firedrake的自动逆功能，包括解复值问题。这将大大有利于用户wishingto模拟涉及电磁波的优化设计问题。第三，我们将扩大网格的范围，Firedrake可以采用包括非结构化六面体网格，和分层细化网格。这将提高Firedrake对高效高阶不连续Galerkin离散化和多尺度问题（如材料折叠）的支持。除了扩展Firedrake的技术能力外，该项目还将发展和支持使用Firedrake的连续介质力学研究人员社区。我们将通过提供主要桌面操作系统的软件包来减少安装Firedrake所需的技术知识。我们将运行教程，研讨会，并提供在线支持，以新的和现有的Firedrakeusers。一个“开放式”的用户访问Firedrake核心开发人员的计划将提供个人一对一的帮助，满足他们的模拟需求。我们将投入大量的时间来扩展和维护Firedrake的高质量文档。

项目成果

Automatic adjoint-based inversion schemes for geodynamics: Reconstructing the evolution of Earth's mantle in space and time

基于自动伴随的地球动力学反演方案：重建地幔在空间和时间上的演化

• DOI: 10.5194/egusphere-2023-2683
• 发表时间: 2023
• 作者: Ghelichkhan S

Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake

将修剪的偶然性方法引入 Firedrake 的计算实践中

• DOI: 10.1145/3490485
• 发表时间: 2022
• 期刊: ACM Transactions on Mathematical Software
• 影响因子: 2.7
• 作者: Crum, Justin;Cheng, Cyrus;Ham, David A.;Mitchell, Lawrence;Kirby, Robert C.;Levine, Joshua A.;Gillette, Andrew
• 通讯作者: Gillette, Andrew

Point Data Assimilation in Firedrake and Icepack

Firedrake 和 Icepack 中的点数据同化

• DOI: 10.5194/egusphere-egu23-12705
• 发表时间: 2023
• 作者: Nixon-Hill R