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Global Convergence Rates of Some Multilevel Methods for Variational and Quasi-Variational Inequalities Read chapter Read first chapter

2017 | OriginalPaper | Chapter

SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation

Authors : Martin J. Gander, Atle Loneland

Published in: Domain Decomposition Methods in Science and Engineering XXIII

Publisher: Springer International Publishing

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Abstract

In domain decomposition methods, coarse spaces are traditionally added to make the method scalable. Coarse spaces can however do much more: they can act on other error components that the subdomain iteration has difficulties with, and thus accelerate the overall solution process. We identify here the optimal coarse space for RAS, where optimal does not refer to scalable, but to best possible. This coarse space leads to convergence of the subdomain iterative method in two steps. Since this coarse space is very rich, we propose an approximation which turns out to be also very effective for multiscale problems.

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previous chapter On the Definition of Dirichlet and Neumann Conditions for the Biharmonic Equation and Its Impact on Associated Schwarz Methods
next chapter Optimized Schwarz Methods for Domain Decompositions with Parabolic Interfaces
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Metadata
Title
SHEM: An Optimal Coarse Space for RAS and Its Multiscale Approximation
Authors
Martin J. Gander
Atle Loneland
Copyright Year
2017
Book
Domain Decomposition Methods in Science and Engineering XXIII

Print ISBN: 978-3-319-52388-0

Electronic ISBN: 978-3-319-52389-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52389-7_32

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