Mathematical software tools for multi-physics simulations (Garth N. Wells, University of Cambridge)

While the complexity and sophistication of physical models addressed in research continually increases, the tools used to build numerical models to solve new problems has not kept pace. Moreover, with increasing model sophistication and the wide-spread and low cost availability of high performance computing resources, it is not reasonable to expect a researcher, or even a small team of researchers, in specific domain to possesses a breadth of expertise that spans computer science, numerical analysis and the application domain itself. I will present a range of software ideas and tools for bridging these gaps. The central concept is to provide domain-specific software abstractions that permit domain experts to expressive numerical models using a syntax that mirrors the technical language of their own domain. This permits domain experts to rapidly and compactly create new, high performance numerical models. By using a high level of abstraction to express a problem, it becomes possible for software libraries to reason intelligently with the problem at hand to create programs that are more efficient that those that could reasonably be produced by an expert by hand. Examples of the approach in the context of the finite element method will be provided, with applications spanning problems in solid mechanics, fluid mechanics and electromagnets.