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On-the-fly Singular Value Decomposition for Aitken's Acceleration of the Schwarz Domain Decomposition Method,

Abstract : This paper discusses the low-rank approximation of the Aitken's acceleration of the convergence of the Schwarz domain decomposition method. The singular value decomposition (SVD) of the solution on interfaces at successive Schwarz iterations gives a basis of a low-dimensional space. The error operator of the Schwarz process, involved in the Aitken's formula, is approximated in this space. The efficiency of the Aitken's acceleration depends on the quality of this basis to approximate the exact solution, which is related to the number of iterations involved in the SVD. We use an iterative procedure to compute the SVD simultaneously with the Schwarz process in order to perform the Aitken's acceleration when the SVD satisfies a mathematical criterion.
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https://hal.archives-ouvertes.fr/hal-00951587
Contributor : Damien Tromeur-Dervout Connect in order to contact the contributor
Submitted on : Tuesday, February 25, 2014 - 9:52:28 AM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM

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  • HAL Id : hal-00951587, version 1

Citation

Laurent Berenguer, Thomas Dufaud, Duc Toan Pham, Damien Tromeur-Dervout. On-the-fly Singular Value Decomposition for Aitken's Acceleration of the Schwarz Domain Decomposition Method,. PARCO11, Sep 2011, Ghent, Belgium. pp.243 - 250. ⟨hal-00951587⟩

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