The development of numerical software in general and finite element
software in particular is recognized as a challenging and error-prone
process -- traditionally requiring in-depth expertise from a number of
scientific fields. The FEniCS and Dolfin-adjoint projects target this
challenge by developing generic algorithms and open source software
for the automated solution of partial differential equations using
finite element methods. The FEniCS Project is described by in the
FEniCS book [1] and a number of research papers, see e.g. [2].

The related Dolfin-adjoint software, winner of the 2015 Wilkinson
Prize for Numerical Software, automatically derives discrete adjoint
and tangent linear models from a forward FEniCS model[3]. These
adjoint and tangent linear models are key ingredients in many
important algorithms, such as data assimilation, optimal control,
sensitivity analysis, design optimisation, and error estimation.

In this presentation, I'll give an overview of the FEniCS and
Dolfin-adjoint projects focusing on current developments and
applications in biomedical computing.

[1] A. Logg, K.-A. Mardal, G. N. Wells et al. (2012). Automated
Solution of Differential Equations by the Finite Element Method,
Springer. [doi:10.1007/978-3-642-23099-8]

[2] M. S. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet,
A. Logg, C. Richardson, J. Ring, M. E. Rognes and G. N. Wells
(2015). The FEniCS Project Version 1.5, Archive of Numerical Software,
3(100), [doi:10.11588/ans.2015.100.20553].

[3] P. E. Farrell, D. A. Ham, S. W. Funke and M. E. Rognes
(2013). Automated derivation of the adjoint of high-level transient
finite element programs, SIAM Journal on Scientific Computing 35.4,
pp. C369-C393. doi:10.1137/120873558.