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:
An Adaptive MFD Method for the Obstacle Problem Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Preconditioning of Elasticity Problems with Discontinuous Material Parameters

Authors : I. Georgiev, J. Kraus

Published in: Numerical Mathematics and Advanced Applications 2011

Publisher: Springer Berlin Heidelberg

Log in

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

search-config
loading …

Abstract

We consider preconditioning methods for the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The presented approach is a generalization of the subspace correction method studied in Ayuso et al. (A Subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations, arXiv:1110.5743v2, 2011) for linear elasticity problems with discontinuous material properties. The application of the preconditioner reduces to the solution of a problem arising from discretization of the equations of linear elasticity by nonconforming Crouzeix-Raviart finite elements plus the solution of a well-conditioned problem on the complementary space.

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 Some Experiences with Multilevel Krylov Methods
next chapter A Robust Preconditioner for Distributed Optimal Control for Stokes Flow with Control Constraints
Literature
1.
B. Ayuso, I. Georgiev, J. Kraus, and L. Zikatanov, A simple preconditioner for the SIPG discretization of linear elasticity equations. In I. Dimov, S. Dimova, and N. Kolkovska, editors, Numerical Methods and Applications, volume 6046 of Lecture Notes in Computer Science, pages 353–360. Springer, Heidelberg, 2011.CrossRef
2.
B. Ayuso, I. Georgiev, J. Kraus, and L. Zikatanov, A Subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations. arXiv:1110.5743v2, 2011.
3.
B. Ayuso, M. Holst, Y. Zhu and L. Zikatanov, Multilevel preconditioners for discontinuous Galerkin approximation of elliptic problems with jump coefficients. arXiv:1012/1287vl, 2010.
4.
Blanca Ayuso de Dios and Ludmil Zikatanov. Uniformly convergent iterative methods for discontinuous Galerkin discretizations. J. Sci. Comput., 40(1–3):4–36, 2009.
5.
R. Blaheta, S. Margenov, and M. Neytcheva, Aggregation-based multilevel preconditioning of non-conforming FEM elasticity problems. In J. Dongarra, K. Madsen, and J. Wasniewski, editors, Applied Parallel Computing, volume 3732 of Lecture Notes in Computer Science, pages 847–856. Springer, Berlin, Heidelberg, 2006.
6.
S. Brenner and L. Scott The mathematical theory of finite element methods. Texts in applied mathematics. vol. 15, Springer-Verlag, 1994.
7.
Susanne C. Brenner and Li-Yeng Sung. Linear finite element methods for planar linear elasticity. Math. Comp., 59(200):321–338, 1992.
8.
F. Brezzi, B. Cockburn, L. D. Marini, and E. Süli. Stabilization mechanisms in discontinuous Galerkin finite element methods. Comput. Methods Appl. Mech. Engrg., 195(25–28):3293–3310, 2006.MathSciNetMATHCrossRef
9.
Richard S. Falk. Nonconforming finite element methods for the equations of linear elasticity. Math. Comp., 57(196):529–550, 1991.
10.
I. Georgiev, J. K. Kraus, and S. Margenov Multilevel preconditioning of Crouzeix-Raviart 3D pure displacement elasticity problems. In I. Lirkov, S. Margenov, and J. Wasniewski, editors, Large Scale Scientific Computing, volume 5910 of Lecture Notes in Computer Science, pages 100–107. Springer, Berlin, Heidelberg, 2010.CrossRef
11.
Peter Hansbo and Mats G. Larson. Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity. M2AN Math. Model. Numer. Anal., 37(1):63–72, 2003.
12.
J. K. Kraus and S. Margenov. Robust Algebraic Multilevel Methods and Algorithms. Radon Series on Computational and Applied Mathematics 5. de Gruyter, October 2009.
Metadata
Title
Preconditioning of Elasticity Problems with Discontinuous Material Parameters
Authors
I. Georgiev
J. Kraus
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Numerical Mathematics and Advanced Applications 2011

Print ISBN: 978-3-642-33133-6

Electronic ISBN: 978-3-642-33134-3

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-33134-3_80

Premium Partner

    Image Credits