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 proceedingpeer-review

16 Citations (Scopus)


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
Number of pages10
ISBN (Electronic)9783319188270
ISBN (Print)9783319188263, 9783319792606
Publication statusPublished - Apr 2016
Event22nd International Conference on Domain Decomposition Methods, DD 2013 - Lugano, Switzerland
Duration: 16 Sept 201320 Sept 2013 (Conference proceedings)

Publication series

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


Conference22nd International Conference on Domain Decomposition Methods, DD 2013
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


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