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Convergence of Substructuring Methods for Elliptic Optimal Control Problems

  • Martin J. GanderEmail author
  • Felix KwokEmail author
  • Bankim C. MandalEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)

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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GenevaGenevaSwitzerland
  2. 2.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong
  3. 3.School of Basic Sciences, Indian Institute of Technology BhubaneswarBhubaneswarIndia

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