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Preprint 04-2009

Solving Time-Dependent Optimal Control Problems in Comsol Multiphysics by Space-Time Discretizations

Source file is available as :   Portable Document Format (PDF)

Author(s) : Ira Neitzel , Uwe Prüfert , Thomas Slawig

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 04-2009

MSC 2000

49K20 Problems involving partial differential equations
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
We use COMSOL Multiphysics to solve time-dependent optimal control problems for partial differential equations whose optimality conditions can be formulated as a PDE. For a class of linear-quadratic model problems we summarize known analytic results on existence of solutions and first order optimality conditions that exhibit the typical feature of time-dependent control problems, namely the fact that a part of the optimality system has to be integrated backward in time. We present a strategy that is based on the treatment of the coupled optimality system in the space-time cylinder. A brief motivation of this approach is given by showing that the optimality system is elliptic in some sence. Numerical examples show advantages and limits of the usage of COMSOL Multiphysics and of our approach.

Keywords : Optimal control of PDEs, finite element method, COMSOL Multiphysics

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