Optimal dirichlet control of partial differential equations on networks

被引：0

作者：

Stoll M. ^{[1
]}

Winkler M. ^{[2
]}

机构：

[1] Chair of Scientific Computing, Technische Universität Chemnitz, Reichenhainer Str. 41, Chemnitz

[2] Chair of Numerical Mathematics (PDEs), Technische Universität Chemnitz, Reichenhainer Str. 41, Chemnitz

来源：

Electronic Transactions on Numerical Analysis | 2020年 / 54卷

关键词：

Complex networks; Error estimation; Optimal Dirichlet control; Preconditioning; Saddle point systems;

D O I：

10.1553/ETNA_VOL54S392

中图分类号：

学科分类号：

摘要：

Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the optimal setup of the differential equation for a given desired state is a challenging numerical analysis task. In this work, we focus on the task of solving an optimization problem subject to a linear differential equation on a metric graph with the control defined on a small set of Dirichlet nodes. We discuss the discretization by finite elements and provide rigorous error bounds as well as an efficient preconditioning strategy to deal with the large-scale case. We show in various examples that the method performs very robustly. Copyright © 2021, Kent State University.

引用

页码：392 / 419

页数：27

共 50 条

[21] On optimal boundary and distributed control of partial integro-differential equations
Khurshudyan, Asatur Zh.
ARCHIVES OF CONTROL SCIENCES, 2014, 24 (01): : 5 - 25
[22] Optimal control of partial differential equations based on the Variational Iteration Method
Akkouche, Abderrahmane
Maidi, Ahmed
Aidene, Mohamed
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 68 (05) : 622 - 631
[23] Domain decomposition in optimal control problems for partial differential equations revisited
Leugering, G
Control Theory of Partial Differential Equations, 2005, 242 : 125 - 155
[24] Optimal control of wave propagation governed by nonlinear partial differential equations
Khasilev, V
APPLIED NONLINEAR DYNAMICS AND STOCHASTIC SYSTEMS NEAR THE MILLENNIUM, 1997, (411): : 24 - 29
[25] REMARKS ON THE DIRICHLET PROBLEM FOR GENERAL LINEAR PARTIAL DIFFERENTIAL EQUATIONS
LITTMAN, W
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1958, 11 (01) : 145 - 151
[26] The Dirichlet problem for higher-order partial differential equations
K. B. Sabitov
Mathematical Notes, 2015, 97 : 255 - 267
[27] A note on the Dirichlet problem for model complex partial differential equations
Ashyralyev, Allaberen
Karaca, Bahriye
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016), 2016, 1759
[28] The Dirichlet problem for higher-order partial differential equations
Sabitov, K. B.
MATHEMATICAL NOTES, 2015, 97 (1-2) : 255 - 267
[29] Solutions of stochastic partial differential equations considered as Dirichlet processes
Denis, L
BERNOULLI, 2004, 10 (05) : 783 - 827
[30] Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
Hintermueller, Michael
Hoppe, Ronald H. W.
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 6454 - 6459

← 1 2 3 4 5 →