TITLE:
Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks
AUTHORS:
Günter Leugering
KEYWORDS:
Optimal Control, Gas Networks, Euler’s Equation, Hierarchy of Models, Semi-Linear Approximation, Non-Overlapping Domain Decomposition
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.8,
August
17,
2017
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.