Adjoint error control: Mathematical analysis and applications in geophysics

CMA, University of Oslo, Norway
(Seminar room B1036, N. H. Abels building)
April 27, 2005.

Speakers:

• Bjørn Gjevik, Department of Mathematics, UiO
• Sebastian Noelle, Department of Mathematics, RWTH Aachen and CMA
• Atle Ommundsen, Norwegian Defence Research
  Establishment, Kjeller, Norway.

Summary:

Adjoint techniques have been used as a powerful technique in mathematics, science and engineering at least since the times of Euler and Lagrange. They have been developed in the fields of linear algebra, calculus and partial differential equations. These techniques are useful if you have a particular goal, like controling an event via the choice of initial or boundary conditions (optimal control) or evaluating and reducing a specific aspect of the error.

After giving a gentle introduction into the mathemtical foundations and some theoretical results in the first lecture, we will focus on some of our own work. Thus the second lecture is on the design of adaptive numerical methods for calculating instationary compressible flows. Here the focus is on the choice of timesteps for implicit schemes. The stability of these schemes allows for rather large timesteps. But how can you guarantee that small waves are still captured, about as well as with an explicit scheme?

The third lecture will be on tidal modals. In a high resolution tidal model boundary conditions are often obtained from models with coarser grid resolution and therefore are subject to errors. Better estimates of the boundary conditions can be obtained by adjusting the model to observational data within the model domain. This leads to an optimization problem with an adjoint model solution and a minimalization of a cost functional. In principle, this approach should work, but in practical problems serious difficulties are often encountered.

Program:

10.15 - 11.00 "Introduction to adjoint error control" (Sebastian Noelle)

11.15 - 12.00 "Timestep control for instationary compressible flow calculations" (Sebastian Noelle)

13.15 - 14.15 "An attempt to optimize tidal models" (Bjørn Gjevik and Atle Ommundsen)