On the time-domain decomposition of parabolic optimal control problems

Wing Hong Felix KWOK

doi:10.1007/978-3-319-52389-7_5

On the time-domain decomposition of parabolic optimal control problems

Wing Hong Felix KWOK^*

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

8 Citations (Scopus)

Abstract

Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXIII
Editors	Hyea Hyun Kim, Axel Klawonn, Eun-Jae Park, Chang-Ock Lee, Olof B. Widlund, Xiao-Chuan Cai, David E. Keyes
Publisher	Springer Verlag
Pages	55-67
Number of pages	13
ISBN (Print)	9783319523880
DOIs	https://doi.org/10.1007/978-3-319-52389-7_5
Publication status	Published - 2017
Event	23rd International Conference on Domain Decomposition Methods, DD23 - Jeju Island, Korea, Republic of Duration: 6 Jul 2015 → 10 Jul 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	116
ISSN (Print)	1439-7358

Conference

Conference	23rd International Conference on Domain Decomposition Methods, DD23
Country/Territory	Korea, Republic of
City	Jeju Island
Period	6/07/15 → 10/07/15

Scopus Subject Areas

Modelling and Simulation
Engineering(all)
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-319-52389-7_5

Cite this

KWOK, W. H. F. (2017). On the time-domain decomposition of parabolic optimal control problems. In H. H. Kim, A. Klawonn, E.-J. Park, C.-O. Lee, O. B. Widlund, X.-C. Cai, & D. E. Keyes (Eds.), Domain Decomposition Methods in Science and Engineering XXIII (pp. 55-67). (Lecture Notes in Computational Science and Engineering; Vol. 116). Springer Verlag. https://doi.org/10.1007/978-3-319-52389-7_5

KWOK, Wing Hong Felix. / On the time-domain decomposition of parabolic optimal control problems. Domain Decomposition Methods in Science and Engineering XXIII. editor / Hyea Hyun Kim ; Axel Klawonn ; Eun-Jae Park ; Chang-Ock Lee ; Olof B. Widlund ; Xiao-Chuan Cai ; David E. Keyes. Springer Verlag, 2017. pp. 55-67 (Lecture Notes in Computational Science and Engineering).

@inproceedings{b4ec1d0ece6e4f8fbafa228140759d14,

title = "On the time-domain decomposition of parabolic optimal control problems",

abstract = "Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.",

author = "KWOK, {Wing Hong Felix}",

year = "2017",

doi = "10.1007/978-3-319-52389-7_5",

language = "English",

isbn = "9783319523880",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer Verlag",

pages = "55--67",

editor = "Kim, {Hyea Hyun} and Axel Klawonn and Eun-Jae Park and Chang-Ock Lee and Widlund, {Olof B.} and Xiao-Chuan Cai and Keyes, {David E.}",

booktitle = "Domain Decomposition Methods in Science and Engineering XXIII",

address = "Germany",

note = "23rd International Conference on Domain Decomposition Methods, DD23 ; Conference date: 06-07-2015 Through 10-07-2015",

}

KWOK, WHF 2017, On the time-domain decomposition of parabolic optimal control problems. in HH Kim, A Klawonn, E-J Park, C-O Lee, OB Widlund, X-C Cai & DE Keyes (eds), Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol. 116, Springer Verlag, pp. 55-67, 23rd International Conference on Domain Decomposition Methods, DD23, Jeju Island, Korea, Republic of, 6/07/15. https://doi.org/10.1007/978-3-319-52389-7_5

On the time-domain decomposition of parabolic optimal control problems. / KWOK, Wing Hong Felix.
Domain Decomposition Methods in Science and Engineering XXIII. ed. / Hyea Hyun Kim; Axel Klawonn; Eun-Jae Park; Chang-Ock Lee; Olof B. Widlund; Xiao-Chuan Cai; David E. Keyes. Springer Verlag, 2017. p. 55-67 (Lecture Notes in Computational Science and Engineering; Vol. 116).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

TY - GEN

T1 - On the time-domain decomposition of parabolic optimal control problems

AU - KWOK, Wing Hong Felix

PY - 2017

Y1 - 2017

N2 - Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.

AB - Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.

UR - http://www.scopus.com/inward/record.url?scp=85016205879&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-52389-7_5

DO - 10.1007/978-3-319-52389-7_5

M3 - Conference proceeding

AN - SCOPUS:85016205879

SN - 9783319523880

T3 - Lecture Notes in Computational Science and Engineering

SP - 55

EP - 67

BT - Domain Decomposition Methods in Science and Engineering XXIII

A2 - Kim, Hyea Hyun

A2 - Klawonn, Axel

A2 - Park, Eun-Jae

A2 - Lee, Chang-Ock

A2 - Widlund, Olof B.

A2 - Cai, Xiao-Chuan

A2 - Keyes, David E.

PB - Springer Verlag

T2 - 23rd International Conference on Domain Decomposition Methods, DD23

Y2 - 6 July 2015 through 10 July 2015

ER -

On the time-domain decomposition of parabolic optimal control problems

Abstract

Publication series

Conference

Scopus Subject Areas

Access to Document

Other files and links

Fingerprint

Cite this