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

该项目将扩展和增强Firedrake自动化有限元模拟系统，使连续介质力学领域的研究人员能够使用比他们自己编写代码更复杂的技术来模拟更广泛的物理现象，并通过嵌入在Python中的高效数学接口来指定模拟。用偏微分方程（PDEs）描述的连续物理系统的模拟是计算科学的主要活动。这跨越了结构的完整性，建立在流体流动上的工业过程的效率，以及从天线传播电磁波等等。每个模拟都需要选择适当的PDE，精确而稳定的离散化，有效的并行组装结果矩阵和向量，以及快速，可扩展的结果数值系统的解决方案。每一个模拟都是一系列过程的组成，每一个过程都是一个研究领域。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，需要在模拟链的每个层次进行更改。挑战在于允许个人研究人员和小团队将他们自己的模拟组合在一起，而不要求每个研究人员都成为过程中每个阶段的实施专家。Firedrake在Python中嵌入了一种数学语言，使研究人员能够以一种高效而简洁的方式编写他们希望执行的模拟。然后由专门的编译器在运行时自动生成仿真的高性能并行实现。其结果是一个系统，科学家和工程师在其中编写数学并得到模拟。这使得研究人员可以专注于手头的连续介质力学问题，而不是创建模拟的力学。Firedrake是一个广泛使用的社区代码，有数百个跨连续介质力学的已发布应用程序。对于许多研究人员来说，firedrake显然已经至少满足了他们的部分需求。然而，连续介质力学研究的复杂性是无限的：总有一些用户和潜在用户的问题无法用Firedrake的高级数学语言完全表达。这个项目将解决几个这样的限制，这些限制是根据过去两年Firedrake用户的正式参与而选择的。首先，我们将扩展Firedrake解决耦合多域系统的能力。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，以包括复值问题。这将大大有利于希望模拟涉及电磁波的最佳设计问题的用户。第三，我们将扩展Firedrake可以使用的网格范围，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。通过提供主要桌面操作系统的软件包，我们将减少安装firedrake所需的技术知识。我们将运行教程，研讨会，并为新的和现有的firedrake用户提供在线支持。用户访问Firedrake核心开发人员的“开放”计划将为他们的模拟需求提供个人一对一的帮助。我们将投入大量时间来扩展和维护Firedrake的高质量文档。

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.