Ira Neitzel, Uwe Prüfert, Thomas Slawig:

Strategies for time-dependent PDE control using an integrated modeling and simulation environment. Part one: problems without inequality constraints

We show how time-dependent optimal control for partial differential equations can be realized in a modern high-level modeling and simulation package. We summarize the general formulation for distributed and boundary control for initial-boundary value problems for parabolic PDEs and derive the optimality system including the adjoint equation. The main difficulty therein is that the latter has to be integrated backwards in time. This implies that complicated implementation effort is necessary to couple state and adjoint equations to compute an optimal solution. Furthermore a large amount of computational effort or storage is required to provide the needed information (i.e the trajectories) of the state and adjoint variables. We show how this can be realized in the modeling and simulation package Comsol Multiphysics(TM), taking advantage of built-in discretization, solver and post-processing technologies and thus minimizing the implementation effort. We present two strategies: The treatment of the coupled optimality system in the space-time cylinder, and the iterative approach by sequentially solving state and adjoint system and updating the controls. Numerical examples show the elegance of the implementation and the efficiency of the two strategies.

Keywords: Optimal control, finite element method

Mail an Jens Burmeister

[Thu Feb 19 18:56:37 2009]

Impressum