Abstract

The derivatives of PDE models are key ingredients in many important algorithms of computational science. They find applications in diverse areas such as sensitivity analysis, PDE -constrained optimisation, continuation and bifurcation analysis, error estimation, and generalised stability theory.

These derivatives, computed using the so-called tangent linear and adjoint models, have made an enormous impact in certain scientific fields (such as aeronautics, meteorology, and oceanography). However, their use in other areas has been hampered by the great practical difficulty of the derivation and implementation of tangent linear and adjoint models. In his recent book, Naumann (2011) describes the problem of the robust automated derivation of parallel tangent linear and adjoint models as “one of the great open problems in the field of high-performance scientific computing”.

In this talk, we present an elegant solution to this problem for the common case where the original discrete forward model may be written in variational form, and discuss some of its applications.