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Spectral Coarse Spaces in Robust Two-Level Schwarz Methods

  • J. WillemsEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 45)

Abstract

A survey of recently proposed approaches for the construction of spectral coarse spaces is provided. These coarse spaces are in particular used in two-level preconditioners. At the core of their construction are local generalized eigenvalue problems. It is shown that by means of employing these spectral coarse spaces in two-level additive Schwarz preconditioners one obtains preconditioned systems whose condition numbers are independent of the problem sizes and problem parameters such as (highly) varying coefficients. A unifying analysis of the recently presented approaches is given, pointing out similarities and differences. Some numerical experiments confirm the analytically obtained robustness results.

Keywords

Spectral coarse space Robust preconditioner Two-level domain decomposition Additive Schwarz Multiscale problems 

Notes

Acknowledgements

The research of J. Willems was supported in parts by NSF Grant DMS-1016525.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Radon Institute for Computational and Applied Mathematics (RICAM)LinzAustria

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