A time-adaptive optimal control approach for 4D-var data assimilation problems governed by parabolic PDEs

Seminar talk followed by a young researcher network meeting.

Abstract:

The common solution techniques of the data assimilation problem typically require the numerical treatment of large systems. Therefore, it is not surprising that the search for strategies to reduce the computational effort for this task, is a focus of various researches.

In this talk, a reformulation of the data assimilation problem governed by a parabolic partial differential equation (pde) will be presented. This reformulation allows to find the solution of the data assimilation problem by solving a fourth order elliptic pde with e.g. finite elements.

The transition between these problems involves the interpretation of the data assimilation task as an optimal control problem and the further utilisation of the arising optimality conditions in order to establish the fourth order system. The idea which motivated the switch between these systems is not only limited to data assimilation, but can also be used for the solution of more general optimal control problems. 

Switching from an optimisation problem to the discretisation of a pde now allows to investigate the problem from a new angle. Strategies from model order reduction or the solution of the problem on adaptive grids are now conceivable and first attempts will be discussed. 

Authors: Carmen Gräßle, Jannis Marquardt