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 proceedingChapterpeer-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 publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Verlag
Pages291-300
Number of pages10
DOIs
Publication statusPublished - 2018

Publication series

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

Scopus Subject Areas

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

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