Achieving robustness through coarse space enrichment in the two level Schwarz framework

Nicole Spillane; Victorita Dolean; Patrice Hauret; Frédéric Nataf; Clemens Pechstein; Robert Scheichl

doi:10.1007/978-3-319-05789-7_42

Achieving robustness through coarse space enrichment in the two level Schwarz framework

Nicole Spillane, Victorita Dolean, Patrice Hauret, Frédéric Nataf, Clemens Pechstein, Robert Scheichl

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

2 Citations (SciVal)

Abstract

As many DD methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation. This is the case in particular if the partition into is not aligned with all jumps in the coefficients. The theoretical analysis traces this lack of robustness back to the so called stable splitting property. In this work we propose to solve a generalized eigenvalue problem in each subdomain which identifies which vectors are responsible for violating the stable splitting property. These vectors are used to span the coarse space and taken care of by a direct solve while all remaining components behave well. The result is a condition number estimate for the two level method which does not depend on the number of subdomains or any jumps in the coefficients.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXI
Subtitle of host publication	Lecture Notes in Computational Science and Engineering
Editors	Jocelyne Erhel , Martin J Gander , Laurence Halpern , Geraldine Pichot , Taiufik Sassi , Olof Widlund
Publisher	Springer
Pages	447-455
Number of pages	10
Volume	98
ISBN (Electronic)	9783319057897
ISBN (Print)	9783319057880
DOIs	https://doi.org/10.1007/978-3-319-05789-7_42
Publication status	Published - 21 Apr 2014
Event	21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 - Rennes, UK United Kingdom Duration: 25 Jun 2012 → 29 Jun 2012

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	98
ISSN (Print)	14397358

Conference

Conference	21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014
Country/Territory	UK United Kingdom
City	Rennes
Period	25/06/12 → 29/06/12

Access to Document

10.1007/978-3-319-05789-7_42

Cite this

Spillane, N., Dolean, V., Hauret, P., Nataf, F., Pechstein, C., & Scheichl, R. (2014). Achieving robustness through coarse space enrichment in the two level Schwarz framework. In J. Erhel , M. J. Gander , L. Halpern , G. Pichot , T. Sassi , & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering (Vol. 98, pp. 447-455). (Lecture Notes in Computational Science and Engineering; Vol. 98). Springer. https://doi.org/10.1007/978-3-319-05789-7_42

Achieving robustness through coarse space enrichment in the two level Schwarz framework. / Spillane, Nicole; Dolean, Victorita; Hauret, Patrice et al.
Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering. ed. / Jocelyne Erhel ; Martin J Gander ; Laurence Halpern ; Geraldine Pichot ; Taiufik Sassi ; Olof Widlund . Vol. 98 Springer, 2014. p. 447-455 (Lecture Notes in Computational Science and Engineering; Vol. 98).

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

Spillane, N, Dolean, V, Hauret, P, Nataf, F, Pechstein, C & Scheichl, R 2014, Achieving robustness through coarse space enrichment in the two level Schwarz framework. in J Erhel , MJ Gander , L Halpern , G Pichot , T Sassi & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering. vol. 98, Lecture Notes in Computational Science and Engineering, vol. 98, Springer, pp. 447-455, 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014, Rennes, UK United Kingdom, 25/06/12. https://doi.org/10.1007/978-3-319-05789-7_42

Spillane N, Dolean V, Hauret P, Nataf F, Pechstein C, Scheichl R. Achieving robustness through coarse space enrichment in the two level Schwarz framework. In Erhel J, Gander MJ, Halpern L, Pichot G, Sassi T, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering. Vol. 98. Springer. 2014. p. 447-455. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-05789-7_42

Spillane, Nicole ; Dolean, Victorita ; Hauret, Patrice et al. / Achieving robustness through coarse space enrichment in the two level Schwarz framework. Domain Decomposition Methods in Science and Engineering XXI : Lecture Notes in Computational Science and Engineering. editor / Jocelyne Erhel ; Martin J Gander ; Laurence Halpern ; Geraldine Pichot ; Taiufik Sassi ; Olof Widlund . Vol. 98 Springer, 2014. pp. 447-455 (Lecture Notes in Computational Science and Engineering).

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Achieving robustness through coarse space enrichment in the two level Schwarz framework

Abstract

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Multiscale Modelling of Aerospace Composites

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Achieving robustness through coarse space enrichment in the two level Schwarz framework

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Projects

Multiscale Modelling of Aerospace Composites

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