Convergence of Substructuring Methods for Elliptic Optimal Control Problems

Martin J. Gander*, Wing Hong Felix KWOK, Bankim C. Mandal

*Corresponding author for this work

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

Abstract

We study in this paper Dirichlet–Neumann and Neumann–Neumann methods for the parallel solution of elliptic optimal control problems. Unlike in the case of single linear or non-linear elliptic problems, we need to solve here two coupled elliptic problems that arise as a part of optimality system for the optimal control problem. We present a rigorous convergence analysis for the case of two non-overlapping subdomains, which shows that both methods converge in at most three iterations. We illustrate our findings with numerical results.

Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIV
EditorsPetter E. Bjørstad, Susanne C. Brenner, Lawrence Halpern, Hyea Hyun Kim, Ralf Kornhuber, Talal Rahman, Olof B. Widlund
PublisherSpringer, Cham
Pages291-300
Number of pages10
Edition1st
ISBN (Electronic)9783319938738
ISBN (Print)9783319938721
DOIs
Publication statusPublished - 5 Jan 2019
Event24th International Conference on Domain Decomposition Methods in Science and Engineering - Svalbard, Norway
Duration: 6 Feb 201710 Feb 2017
http://www.ddm.org/dd24/

Publication series

NameLecture Notes in Computational Science and Engineering
Volume125
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Conference

Conference24th International Conference on Domain Decomposition Methods in Science and Engineering
Abbreviated titleDD2017
Country/TerritoryNorway
CitySvalbard
Period6/02/1710/02/17
Internet address

Scopus Subject Areas

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

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