Solving Time-Dependent Optimal Control Problems in COMSOL Multiphysics

I. Neitzel[1], U. Prüfert[2], and T. Slawig[3]
[1]DFG priority program SPP 1253, Technische Universität Berlin, Berlin, Germany
[2]DFG research center Matheon, Technische Universität Berlin, Germany
[3]DFG Cluster of Excellence The Future Ocean, DFG priority progam SPP 1253, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
Published in 2008

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. Numerical examples show advantages and limits of the usage of COMSOL Multiphysics and of our approach.

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