Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

• 作者: Günter Leugering
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Optimal Control Gas Networks Euler’s Equation HIERARCHY of Models SEMI-LINEAR APPROXIMATION Non-Overlapping DOMAIN DECOMPOSITION
• 年，卷（期）: 2017,（8）
• 页码范围: 1074-1099
• 页数: 26页
• 分类号: O1

摘要

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.