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Automating Finite Element Simulation by Generating Tensor Computations from Vector Calculus

David Ham ( Imperial )

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.

Speaker bio

Dr David Ham is a reader in Computational Mathematics at Imperial College London. He has degrees in mathematics and law from the Australian National University, and a doctorate in numerical methods for PDEs from TU Delft. His research focusses on automating the finite element method, and focuses on the Firedrake automated simulation system. He received the 1995 Wilkinson Prize for Numerical Software for his automation of inverse finite element simulation. Dr Ham co-leads the joint mathematics and computer science degree programme at Imperial College London, and founded and leads the Mary Lister McCammon Summer Research Fellowship for Women in Mathematics and Statistics. He is the chief executive editor of the European Geosciences Union journal Geoscientific Model Development.




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