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A non-overlapping DDM combined with the characteristic method for optimal control problems governed by convection–diffusion equations

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  • Tongjun Sun

    (Shandong University)

  • Keying Ma

    (Shandong University)

Abstract

In this paper, we consider a non-overlapping domain decomposition method combined with the characteristic method for solving optimal control problems governed by linear convection–diffusion equations. The whole domain is divided into non-overlapping subdomains, and the global optimal control problem is decomposed into the local problems in these subdomains. The integral mean method is utilized for the diffusion term to present an explicit flux calculation on the inter-domain boundary in order to communicate the local problems on the interfaces between subdomains. The convection term is discretized along the characteristic direction. We establish the fully parallel and discrete schemes for solving these local problems. A priori error estimates in $$L^2$$ L 2 -norm are derived for the state, co-state and control variables. Finally, we present numerical experiments to show the validity of the schemes and verify the derived theoretical results.

Suggested Citation

  • Tongjun Sun & Keying Ma, 2018. "A non-overlapping DDM combined with the characteristic method for optimal control problems governed by convection–diffusion equations," Computational Optimization and Applications, Springer, vol. 71(1), pages 273-306, September.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:1:d:10.1007_s10589-018-0008-0
    DOI: 10.1007/s10589-018-0008-0
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    References listed on IDEAS

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    1. J. D. Benamou, 1999. "Domain Decomposition, Optimal Control of Systems Governed by Partial Differential Equations, and Synthesis of Feedback Laws," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 15-36, July.
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