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Two-level Schwarz methods with coarse spaces based on Dirichlet-to-Neumann maps

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HAL Id: inria-00581741

https://hal.inria.fr/inria-00581741

Submitted on 31 Mar 2011

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Two-level Schwarz methods with coarse spaces based on

Dirichlet-to-Neumann maps

Frédéric Nataf, Victorita Dolean, Robert Scheichl, Hua Xiang

To cite this version:

Frédéric Nataf, Victorita Dolean, Robert Scheichl, Hua Xiang. Two-level Schwarz methods with coarse spaces based on Dirichlet-to-Neumann maps. International Conference On Preconditioning Techniques For Scientific And Industrial Applications, Preconditioning 2011, May 2011, Bordeaux, France. �inria-00581741�

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Two-level Schwarz methods with coarse spaces based on

Dirichlet–to–Neumann maps

List of authors: F. Nataf 1 V. Dolean 2 R. Scheichl 3 H. Xiang 4

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established. We consider problems with high contrasts in the coefficients. We construct the coarse space using the low frequency modes of the subdomain DtN maps. A theoretical estimate of the condition number of the additive Schwarz method (ASM) enables us to select the necessary eigenvectors to be added to the coarse space in order to have a convergence rate of the order of the constant coefficient case. Our method is suitable for the parallel implementation. Its efficiency is demonstrated by numerical examples on problems with high heterogeneities for both manual and automatic partitionings.

1

CNRS, France. [email protected]

2

Universit´e de Nice, France. [email protected]

3

University of Bath, United Kingdom. [email protected]

4

Wuhan University, China. [email protected]

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