A Crank-Nicholson Domain Decomposition Method for Optimal Control Problem of Parabolic Partial Differential Equation

  • Jixin ChenEmail author
  • Danping YangEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)


A parallel domain decomposition algorithm is considered for solving an optimal control problem governed by a parabolic partial differential equation. The proposed algorithm relies on non-iterative and non-overlapping domain decomposition, which uses some implicit sub-domain problems and explicit flux approximations at each time step in every iteration. In addition, outer iterations are introduced to achieve the parallelism. Numerical experiments are supplied to show the efficiency of our proposed method.


  1. 1.
    J. Chen, D. Yang, Explicit/implicit and Crank-Nicolson domain decomposition methods for parabolic partial differential equations (revised)Google Scholar
  2. 2.
    J. Chen, D. Yang, Parallel Crank-Nicolson and Dawson-Dupont type domain decomposition procedure for optimal control problem governed by parabolic equation (in preparation)Google Scholar
  3. 3.
    C.N. Dawson, T.F. Dupont, Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems. Math. Comput. 58(197), 21–34 (1992)MathSciNetCrossRefGoogle Scholar
  4. 4.
    K. Ma, T. Sun, Galerkin domain decomposition procedures for parabolic equations on rectangular domain. Int. J. Numer. Methods Fluids 62(4), 449–472 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    D. Yang, Parallel domain decomposition procedures of improved D-D type for parabolic problems. Comput. Appl. Math. 233(11), 2779–2794 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    B. Zhang, J. Chen, D. Yang, Parallel D-D type domain decomposition algorithm for optimal control problem governed by parabolic partial differential equation. J. Numer. Math. 25(1), 35–53 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsEast China Normal UniversityShanghaiChina
  2. 2.Department of MathematicsUniversité libre de BruxellesBrusselsBelgium

Personalised recommendations