Abstract
In this paper, we study robust two-level domain decomposition preconditioners for highly anisotropic multiscale problems. We present a construction of coarse spaces that emploies initial multiscale basis functions and discuss techniques to achieve smaller dimensional coarse spaces without sacrificing the robustness of the preconditioner. We also present numerical results and consider possible extensions of these approaches where the dimension of the coarse space can be reduced further.
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Bibliography
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Acknowledgements
The work of all authors has been partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The work of RL has been supported in part by the US NSF Grant DMS-1016525. The work of SM was partially supported by the Bulgarian NSF Grant DO 02-147/08. The work of YE has been supported by the DOE and NSF (DMS 0934837, DMS 0902552, and DMS 0811180).
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Efendiev, Y., Galvis, J., Lazarov, R., Margenov, S., Ren, J. (2013). Multiscale Domain Decomposition Preconditioners for Anisotropic High-Contrast Problems. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_33
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DOI: https://doi.org/10.1007/978-3-642-35275-1_33
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