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Soft Computing for Problem Solving pp 485–494Cite as

Substructuring Waveform Relaxation Methods for Parabolic Optimal Control Problems

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 817))

Abstract

We study in this paper Dirichlet–Neumann and Neumann–Neumann waveform relaxation methods for the parallel solution of linear-quadratic parabolic optimal control problems, originating from the examples of transient optimal heating with distributed control. Unlike in the case of single linear or nonlinear parabolic problem, we need to solve here two coupled parabolic problems that arise as a part of optimality system for the optimal control problem. We present the detail algorithms for the case of two non-overlapping subdomains and show conditional convergence properties in few special cases. We illustrate our findings with numerical results.

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Acknowledgements

I would like to express my gratitude to Prof. Martin J. Gander and Prof. Felix Kwok for their constant support and stimulating suggestions.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, 752050, Odisha, India

    Bankim C. Mandal

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  1. Bankim C. Mandal
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Correspondence to Bankim C. Mandal .

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Editors and Affiliations

  1. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  2. Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, India

    Kedar Nath Das

  3. Department of Mathematics and Computer Science, Faculty of Science, Liverpool Hope University, Liverpool, UK

    Atulya Nagar

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Kusum Deep

  5. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, Odisha, India

    Akshay Kumar Ojha

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Mandal, B.C. (2019). Substructuring Waveform Relaxation Methods for Parabolic Optimal Control Problems. In: Bansal, J., Das, K., Nagar, A., Deep, K., Ojha, A. (eds) Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 817. Springer, Singapore. https://doi.org/10.1007/978-981-13-1595-4_39

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