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:
Weighted Residuals and Galerkin’s Method for a Generic 1D Problem Read chapter Read first chapter

2018 | OriginalPaper | Chapter

5. Iterative Solutions Schemes

Author : Tarek I. Zohdi

Published in: A Finite Element Primer for Beginners

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

There are two main approaches to solving systems of equations resulting from numerical discretization of solid mechanics problems, direct and iterative.

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 Accuracy of the Finite Element Method in One Dimension
next chapter Weak Formulations in Three Dimensions
Footnotes
1
However, specialized direct sparse solvers can be used if the matrices have a special structure.
 
2
For example, Gaussian elimination is approximately
$$\begin{aligned} 2(N+(N-1)^2+(N-2)^2+(N-3)^2+ ... 1^2)=2\sum _{k=1}^Nk^2\approx 2\int _0^Nk^2dk=\frac{2}{3}N^3. \end{aligned}$$
(5.2)
An operation such as the addition of two numbers, or multiplication of two numbers, is one operation count.
 
3
Similar iterative solvers can be developed for unsymmetric systems, and we refer the reader to Axelsson [1] for details.
 
Literature
1.
Axelsson, O. (1994). Iterative solution methods. Cambridge: Cambridge University Press.
Metadata
Title
Iterative Solutions Schemes
Author
Tarek I. Zohdi
Copyright Year
2018
Book
A Finite Element Primer for Beginners

Print ISBN: 978-3-319-70427-2

Electronic ISBN: 978-3-319-70428-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-70428-9_5

Premium Partners

    Image Credits