Abstract

Domain specific languages (DSLs) can allow ordinary users to easily and efficiently implement new algorithms without a domain expert at their side. Applications areas with modern DSLs in the computational sciences include Bayesian inference problems (Stan http://mc-stan.org) and the finite element method (Unified Form Language http://fenicsproject.org).

In this talk I will show how we have used the high-level Unified Form Language (UFL) to concisely and expressively declare finite element solvers for the thin structural theories, widely used throughout engineering, applied mechanics and physics to simulate objects like beams, plates and shells (https://bitbucket.org/unilucompmech/fenics-shells). UFL was not designed with this specific application in mind, but because of the generality of the abstractions available we have been able to implement these quite complex models relatively straightforwardly.

I will further motivate the advantages of this high-level way of working by showing how sensitivities of finite element models can be easily calculated via automatic symbolic differentiation techniques (http://www.dolfin-adjoint.org). This easy calculation is a direct consequence of the high-level representation of the problem. We are currently using these sensitivities in Monte Carlo methods to greatly accelerate the propagation of uncertainty through complex physical systems in both fluid and solid mechanics.

FEniCS-Shells is joint work with Matteo Brunetti, Stéphane P. A. Bordas and Corrado Maurini.

Using automatic derivatives to accelerate the convergence of stochastic PDEs is joint work with Paul Hauseux and Stéphane P. A. Bordas.