Publikation: Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems
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This paper is concerned with a novel convergence analysis of the optimized Schwarz waveform relaxation method (OSWRM) for the solution of optimal control problems governed by periodic parabolic partial differential equations (PDEs). The new analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition. This leads to a precise characterization of the convergence factor of the method at the semidiscrete level. Using this characterization, the optimal transmission condition parameter is obtained at the semidiscrete level and its asymptotic behavior as the time discretization converges to zero is analyzed in detail.
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CIARAMELLA, Gabriele, Laurence HALPERN, Luca MECHELLI, 2024. Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems. In: Journal of Computational Physics. Elsevier. 2024, 496, 112572. ISSN 0021-9991. eISSN 1090-2716. Available under: doi: 10.1016/j.jcp.2023.112572BibTex
@article{Ciaramella2024-01Conve-68842, year={2024}, doi={10.1016/j.jcp.2023.112572}, title={Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems}, volume={496}, issn={0021-9991}, journal={Journal of Computational Physics}, author={Ciaramella, Gabriele and Halpern, Laurence and Mechelli, Luca}, note={Article Number: 112572} }
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