Abstract
In this work, we consider the coupled systems of a partial differential equations, which arise in the modeling of thermoelasticity processes in heterogeneous domains. Heterogeneity of the properties requires a high resolution solve that adds many degrees of freedom that can be computationally costly. For the numerical solution, we use a Generalized Multiscale Finite Element Method (GMsFEM) that solves problem on a coarse grid by constructing local multiscale basis functions [1,2,3]. We construct multiscale basis functions for the temperature and for the displacements on the offline stage in each coarse block using local spectral problems [4,5,6,7]. On the online stage we construct coarse scale system using precalculated multiscale basis functions and solve problem with any forcing and boundary conditions. The numerical results are presented for heterogeneous and perforated domains.
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Acknowledgement
We would like to thank Professor Yalchin Efendiev for many interesting discussions. This work is partially supported by the grant of the President of the Russian Federation MK-9613.2016.1 and RFBR (project N 15-31-20856).
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Vasilyeva, M., Stalnov, D. (2017). A Generalized Multiscale Finite Element Method for Thermoelasticity Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_82
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DOI: https://doi.org/10.1007/978-3-319-57099-0_82
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