Automating forward and inverse finite element simulation in Firedrake and Dolfin-adjoint

Abstract: Simulating continuous systems modelled by PDEs underpins much of computational science and engineering. Each simulation is a complex combination of PDEs, parametrisations, discretisations, preconditioners and solvers. The precise combination that is optimal is different for each application and changes with the hardware, or as further advances in numerical mathematics are made. Many (possibly most) simulation challenges in science and engineering are actually inverse problems in which parameters are sought, sensitivities analysed and/or data assimilated.

Here I will present Firedrake, an automated system for generating numerical solutions to PDEs from a high level mathematical specification. I will examine some of the capabilities of the system before lifting the lid on the sequence of automated mathematical transformations that make it possible. I will also cover the interaction with dolfin-adjoint to produce gradients of solution functionals by solving the adjoint PDE.

computational biologycomputational engineering, finance, and sciencenumerical analysiscomputational physics

Audience: researchers in the topic

ANU Mathematics and Computational Sciences Seminar