  


Nonoverlapping Domain Decomposition for Optimal Control Problems governed by Semilinear Models for Gas Flow in Networks
Günter Leugering(guenter.leugeringfau.de) Abstract: We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a firstorder system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller subgraphs  ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding timediscrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system. Keywords: Optimal control, Gas networks, Euler's equation, Semilinear PDE, Nonoverlapping domain decomposition Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Category 2: Applications  Science and Engineering Citation: Download: [PDF] Entry Submitted: 11/16/2017 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  