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Multiscale finite elements for linear elasticity: Oscillatory boundary conditions

: Buck, M.; Iliev, O.; Andrä, H.


Erhel, J.:
Domain Decomposition Methods in Science and Engineering XXI : Proceedings of the 21st International Conference on Domain Decomposition Methods; Inria Rennes center, France, June 25–29, 2012
Cham: Springer International Publishing, 2014 (Lecture notes in computational science and engineering 98)
ISBN: 978-3-319-05788-0 (Print)
ISBN: 978-3-319-05789-7 (Online)
ISBN: 3-319-05788-X
International Conference on Domain Decomposition Methods <21, 2012, Rennes>
Conference Paper
Fraunhofer ITWM ()

We extend the multiscale finite element method with oscillatory boundary conditions, introduced for scalar elliptic PDEs by Hou and Wu (J. Comput. Phys. 134:169–189, 1997), to the system of anisotropic linear elasticity. We apply the approach for the construction of robust coarse spaces in the context of two-level overlapping domain decomposition preconditioners for multi-phase elastic composites. We explain the construction on a tetrahedral mesh and present numerical results for isotropic materials showing that robustness w.r.t. coefficient variations in the PDE can be achieved even for the class of problems where inclusions of high stiffness cross coarse element boundaries.