Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Robust Block Preconditioners for Biot’s Model Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Does SHEM for Additive Schwarz Work Better than Predicted by Its Condition Number Estimate?

Authors : Petter E. Bjørstad, Martin J. Gander, Atle Loneland, Talal Rahman

Published in: Domain Decomposition Methods in Science and Engineering XXIV

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The SHEM (Spectral Harmonically Enriched Multiscale) coarse space is a new coarse space for arbitrary overlapping or non-overlapping domain decomposition methods.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Restricted Additive Schwarz Method for Some Inequalities Perturbed by a Lipschitz Operator
next chapter Two-Level Preconditioners for the Helmholtz Equation
Footnotes
1
Any other Sturm Liuville problem could be used as well to get a different variant of SHEM, for example more expensive Schur complements corresponding to the Dirichlet to Neumann maps [11], or one could construct even cheaper interface basis functions without eigenvalue problem, see [8].
 
Literature
1.
J. Aarnes, T.Y. Hou, Multiscale domain decomposition methods for elliptic problems with high aspect ratios. Acta Math. Appl. Sin. Engl. Ser. 18(1), 63–76 (2002)MathSciNetCrossRef
2.
E. Eikeland, L. Marcinkowski, T. Rahman, Overlapping schwarz methods with adaptive coarse spaces for multiscale problems in 3D (2016). Arxiv:1611.00968
3.
M.J. Gander, L. Halpern, Méthodes de décomposition de domaine. Encyclopédie électronique pour les ingénieurs (2012)
4.
M.J. Gander, A. Loneland, SHEM: an optimal coarse space for RAS and its multiscale approximation, in Domain Decomposition Methods in Science and Engineering XXIII (Springer, Berlin, 2016)
5.
M.J. Gander, B. Song, Complete, optimal and optimized coarse spaces for AS, in Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering (Springer, Cham, 2018)
6.
M.J. Gander, L. Halpern, K. Santugini Repiquet, Discontinuous coarse spaces for DD-methods with discontinuous iterates, in Domain Decomposition Methods in Science and Engineering XXI (Springer, Berlin, 2014), pp. 607–615MATH
7.
M.J. Gander, L. Halpern, K. Santugini Repiquet, A new coarse grid correction for RAS/AS, in Domain Decomposition Methods in Science and Engineering XXI (Springer, Berlin, 2014), pp. 275–283MATH
8.
M.J. Gander, A. Loneland, T. Rahman, Analysis of a new harmonically enriched multiscale coarse space for domain decomposition methods (2015). Arxiv preprint arXiv:1512.05285
9.
M.J. Gander, L. Halpern, K. Santugini Repiquet, On optimal coarse spaces for domain decomposition and their approximation, in Domain Decomposition Methods in Science and Engineering XXIV. Lecture Notes in Computational Science and Engineering (Springer, Cham, 2018)
10.
I.G. Graham, P.O. Lechner, R. Scheichl, Domain decomposition for multiscale PDEs. Numer. Math. 106(4), 589–626 (2007)MathSciNetCrossRef
11.
A. Heinlein, A. Klawonn, J. Knepper, O. Rheinbach, Multiscale coarse spaces for overlapping Schwarz methods based on the ACMS space in 2D. Electron. Trans. Numer. Anal. 48, 156–182 (2018)MathSciNetCrossRef
12.
A. Klawonn, P. Radtke, O. Rheinbach, FETI-DP methods with an adaptive coarse space. SIAM J. Numer. Anal. 53(1), 297–320 (2015)MathSciNetCrossRef
13.
N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein, R. Scheichl, Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps. Numer. Math. 126(4), 741–770 (2014)MathSciNetCrossRef
Metadata
Title
Does SHEM for Additive Schwarz Work Better than Predicted by Its Condition Number Estimate?
Authors
Petter E. Bjørstad
Martin J. Gander
Atle Loneland
Talal Rahman
Copyright Year
2018
Book
Domain Decomposition Methods in Science and Engineering XXIV

Print ISBN: 978-3-319-93872-1

Electronic ISBN: 978-3-319-93873-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-93873-8_10

Premium Partner

    Image Credits