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Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks
Chair of Applied Mathematics II, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany
- 1 Chair of Applied Mathematics II, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany
Applied Mathematics·Volume 08 (2017)·Pages 1074–1099·Published 7 August 2017·DOI10.4236/am.2017.88082
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Abstract
We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.
KeywordsOptimal ControlGas NetworksEuler’s EquationHierarchy of ModelsSemi-Linear ApproximationNon-Overlapping Domain Decomposition
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