On the scalability of the time-space multiscale LATIN method

Abstract : The simulation of complex structures at a fine scale, for instance the study of large structures with local cracking or local buckling, leads to systems with a very large number of degrees of freedom and the corresponding calculation cost is generally prohibitive. Dedicated strategies have been developed to make possible the accounting of the very different scales which can appear in this kind of problems, and to take advantage of parallel computer systems. In \cite{ladeveze03b}, a multiscale computational strategy has been proposed for the analysis of structures which are described at a fine scale, both in time and space. This strategy, based on the LArge Time INcrement method (LATIN method \cite{ladeveze99}), can be seen as a mixed domain decomposition strategy in space, including automatic space and time homogenization, and for which no periodicity condition is needed. The first step consists in splitting the structure into sub-structures and interfaces, and dividing the studied time interval into coarse sub-intervals. Interface fields are separated into a macro part and a micro part. Thanks to Saint-Venant's principle, an adapted choice of macro quantities combined with the resolution of a global macro problem, ensures that micro quantities have only local effects. This choice provides to the method numerical scalability in space. The aim of this work is to present an approach \cite{ladeveze09} to extend this property to time aspects. We first present the bases of this approach and the numerical techniques used to solve the micro and macro problems. Then, the choice of the time macro quantities is discussed. A general technique is proposed to adapt the definition of the time scales automatically along the iterations of the algorithm. We show that this technique is efficient and confers robustness to the strategy. Finally, the capabilities of the method are discussed through 3D numerical illustrations.
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https://hal.archives-ouvertes.fr/hal-02025341
Contributor : Jean-Charles Passieux <>
Submitted on : Tuesday, February 19, 2019 - 4:04:43 PM
Last modification on : Friday, May 17, 2019 - 1:23:54 AM

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  • HAL Id : hal-02025341, version 1

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Jean-Charles Passieux, Pierre Ladevèze, David Néron. On the scalability of the time-space multiscale LATIN method. USNCCM 10-10th US National Congress of Computational Mechanics., 2009, Columbus, Ohio, United States. ⟨hal-02025341⟩

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