Schwarz methods for the time-parallel solution of parabolic control problems

Martin J. Gander, Wing Hong Felix Kwok*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

6 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, and a natural idea is to apply Schwarz preconditioners to the large space-time discretized problem. The performance of Schwarz preconditioners for elliptic problems is well understood, but how do such preconditioners perform on discretized parabolic control problems? We present a convergence analysis for a class of Schwarz methods applied to a model parabolic optimal control problem. We show that just applying a classical Schwarz method in time already implies better transmission conditions than the ones usually used in the elliptic case, and we propose an even better variant based on optimized Schwarz theory.
Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXII
EditorsThomas Dickopf, Martin J. Gander, Laurence Halpern, Rolf Krause, Luca F. Pavarino
PublisherSpringer Cham
Pages207-216
Number of pages10
Edition1st
ISBN (Electronic)9783319188270
ISBN (Print)9783319188263, 9783319792606
DOIs
Publication statusPublished - Apr 2016
Event22nd International Conference on Domain Decomposition Methods, DD 2013 - Lugano, Switzerland
Duration: 16 Sep 201320 Sep 2013
https://link.springer.com/book/10.1007/978-3-319-18827-0 (Conference proceedings)

Publication series

NameLecture Notes in Computational Science and Engineering
Volume104
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference22nd International Conference on Domain Decomposition Methods, DD 2013
Country/TerritorySwitzerland
CityLugano
Period16/09/1320/09/13
Internet address

Scopus Subject Areas

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

User-Defined Keywords

  • Classical and optimized Schwarz methods
  • Domain decomposition
  • Parabolic control problems

Fingerprint

Dive into the research topics of 'Schwarz methods for the time-parallel solution of parabolic control problems'. Together they form a unique fingerprint.

Cite this