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Article

Krupička, Lukáš ; Beneš, Michal
An asynchronous three-field domain decomposition method for first-order evolution problems. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 118-123
MSC: 65M55
Keywords:
asynchronous domain decomposition; time-stepping; first-order evolution problem
Summary:
We present an asynchronous multi-domain time integration algorithm with a dual domain decomposition method for the initial boundary-value problems for a parabolic equation. For efficient parallel computing, we apply the three-field domain decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. The implicit method for time discretization and the multi-domain spatial decomposition enable us to use different time steps (subcycling) on different parts of a computational domain, and thus efficiently capture the underlying physics with less computational effort. We illustrate the performance of the proposed multi-domain time integrator by means of a simple numerical example.
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