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Domain Decomposition Methods in Science and Engineering XX pp 467–474Cite as

Two-Grid LNKSz for Distributed Control of Unsteady Incompressible Flows

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

The distributed control of unsteady incompressible flows has been the focus of intense research in scientific computing in the past few years. Most of the existing approaches for distributed control problems are based on the so-called reduced space method which is easier to implement but may have convergence issues in some situations. In this paper we investigate some fully coupled parallel two-grid Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithms for the implicit solution of distributed control problems. In the full space approach we couple the control variables, the state variables and the adjoint variables in a single large system of nonlinear equations. Numerical experiments are presented to show the efficiency and scalability of the algorithm on supercomputers with more than one thousand processors.

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Author information

Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, P. R. China

    Haijian Yang

  2. Department of Computer Science, University of Colorado at Boulder, Boulder, CO, 80309, USA

    Xiao-Chuan Cai

Authors
  1. Haijian Yang
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  2. Xiao-Chuan Cai
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Corresponding author

Correspondence to Haijian Yang .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Randolph Bank

  2. , Department of Mathematics, University of California, San Diego, Gilman Drive 9500, La Jolla, 92093-0112, California, USA

    Michael Holst

  3. , Courant Institute of Mathematical, New York University, Mercer Street 251, New York, 10012-1185, New York, USA

    Olof Widlund

  4. , Department of Mathematics, Pennsylvania State University, State College, 16802, Pennsylvania, USA

    Jinchao Xu

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Yang, H., Cai, XC. (2013). Two-Grid LNKSz for Distributed Control of Unsteady Incompressible Flows. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_55

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