Abstract
We developed parallel time domain decomposition methods to solve systems of linear ordinary differential equations (ODEs) based on the Aitken-Schwarz [5] or primal Schur complement domain decomposition methods [4]. The methods require the transformation of the initial value problem in time defined on ]0, T] into a time boundary values problem. Let f(t, y(t)) be a function belonging to \(\mathcal{C}^{1}(\mathbb{R}^{+}, \mathbb{R}^{d})\) and consider the Cauchy problem for the first order ODE:
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Acknowledgements
This work was supported by the French National Agency of Research through the project ANR MONU-12-0012 H2MNO4. This work was granted access to the HPC resources of CINES under the allocation 2014-c2014066099 made by GENCI (Grand Equipement National de Calcul Intensif) and 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. (2016). Dual Schur Method in Time for Nonlinear ODE. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_59
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DOI: https://doi.org/10.1007/978-3-319-18827-0_59
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