Optimal control of the convergence rate of Global-in-time Schwarz algorithms

Florian Lemarié (1) , Laurent Debreu (2) , Eric Blayo (2)

1 IGPP - Institute of Geophysics and Planetary Physics [Los Angeles]
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

In this study we present a global-in-time non-overlapping Schwarz 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.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Florian Lemarié, Laurent Debreu, Eric Blayo. Optimal control of the convergence rate of Global-in-time Schwarz algorithms. Bank, R. and Holst, M. and Widlund, O. and Xu, J. Domain Decomposition Methods in Science and Engineering XX, Springer-Verlag Berlin Heidelberg, pp.599-606, 2013, volume 91 of Lecture Notes in Computational Science and Engineering, ⟨10.1007/978-3-642-35275-1_71⟩. ⟨hal-00661979v2⟩