Automated calculation of higher order partial differential equation constrained derivative information

Developments in automated code generation have allowed extremely compact representations of numerical models, and also for associated adjoint models to be derived automatically via high level algorithmic differentiation. In this article these principles are extended to enable the calculation of higher order derivative
information. The higher order derivative information is computed through the automated derivation of tangent linear equations, which are then treated as new forward equations, and from which higher order tangent-linear and adjoint information can be derived. The principal emphasis is on the calculation of partial differential equation constrained Hessian actions, but the approach generalises for derivative information at arbitrary order. The derivative calculations are further combined with an advanced data checkpointing strategy. Applications which make use of partial differential equation constrained Hessian actions are presented.