Summary
In this study we present a non-overlapping Schwarz waveform relaxation method applied to the one dimensional unsteady diffusion equation. We derive efficient interface conditions using an optimal control approach once the problem is discretized. Those conditions are compared to the usual optimized conditions derived at the PDE level by solving a min-max problem. The performance of the proposed methodology is illustrated by numerical experiments.
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Acknowledgements
This research was partially supported by the ANR project COMMA (COupling in Multi-physics and multi-scale problems: Models and Algorithms) and by the INRIA project-team MOISE (Modelling, Observation and Identification for Environmental Sciences). We are thankful to Héloïse Pelen (ENS Lyon) for her contribution during her masters internship.
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Lemarié, F., Debreu, L., Blayo, E. (2013). Optimal Control of the Convergence Rate of Schwarz Waveform Relaxation Algorithms. 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_71
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DOI: https://doi.org/10.1007/978-3-642-35275-1_71
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