Automating Finite Element Simulation by Generating Tensor Computations from Vector Calculus

The simulation of continuous physical systems described by Partial Differential Equations (PDEs) has been and continues to be one of the great challenges of scientific computing. From nanomaterials to the weather forecast, the ability to simulate and optimise continuous systems underpins much of science and engineering. From a software perspective, the creation of simulation tools requires the complex manipulation of the PDEs involved, then their discretisation, and finally the optimal scheduling of the resulting calculation. In this talk I will show how the various stages of this tool creation process can be modelled as tensor computations, and that each stage can be automatically generated from the previous one using specialised compiler technology. The result is that scientists and engineers can formulate advanced numerical methods for ever-changing PDEs, and have high performance computational tools generated automatically. This brings both productivity and performance to the simulation problem, enabling scientists to undertake work that would previously have exceeded their human and computational resources.