Abstract
In this paper, we propose a right transmission condition for the time decomposition that consists to transform the initial boundary value problem into a time boundary values problem. This allows us to use classical multiplicative Schwarz algorithm using non overlapping time slices. It also avoids the symmetrizing of the time interval needed to set the unknown value of the solution at the end time boundary of the last time slice. We show that, for nonlinear scalar problems, we must imposed some invariant of the problem as transmission conditions between time slices. We derive a Robin transmission condition in order to break the sequentiality of the propagating of the exact solution from the first time slice to the time slices that follow. We show the purely linear behavior of this multiplicative Schwarz and its extrapolation to the right transmission conditions using the Aitken’s acceleration of the convergence technique.
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Acknowledgements
This work was supported by the French National Agency of Research through the project ANR-12-MONU-0012 H2MNO4. Second author was backed to the Région Rhône-Alpes. This work used the HPC resources of Center for the Development of Parallel Scientific Computing (CDCSP) of University Lyon 1.
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Linel, P., Tromeur-Dervout, D. (2014). Nonlinear Transmission Conditions for time Domain Decomposition Method. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_94
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DOI: https://doi.org/10.1007/978-3-319-05789-7_94
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