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

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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.