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 in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

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 languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXI
Subtitle of host publicationLecture Notes in Computational Science and Engineering
EditorsJocelyne Erhel , Martin J Gander , Laurence Halpern , Geraldine Pichot , Taiufik Sassi , Olof Widlund
PublisherSpringer
Pages447-455
Number of pages10
Volume98
ISBN (Electronic)9783319057897
ISBN (Print)9783319057880
DOIs
Publication statusPublished - 21 Apr 2014
Event21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 - Rennes, UK United Kingdom
Duration: 25 Jun 201229 Jun 2012

Publication series

NameLecture Notes in Computational Science and Engineering
Volume98
ISSN (Print)14397358

Conference

Conference21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014
CountryUK United Kingdom
CityRennes
Period25/06/1229/06/12

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