Advertisement

Fully Implicit Methods for Systems of PDEs

  • Å. Ødegård
  • H. P. Langtangen
  • A. Tveito
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 33)

Abstract

Operator splitting is a common method for solving systems of partial differential equations. This is particularly the case if the system is composed of separate equations for which suitable software already exists. In such cases, operator splitting combined with explicit time-stepping is a straight forward approach. However, for some systems, implicit time-stepping is to be preferred because of better stability properties. The problem of combining existing codes in a fully implicit manner is much harder than the explicit case. The purpose of the present chapter is to discuss some examples illustrating the possibilities of combining existing codes in an implicit manner.

Keywords

Newton Iteration Implicit Method Operator Splitting Jacobi Method Implicit Solver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. J. Holm, A. M. Bruaset, and H. P. Langtangen. Increasing the reliability and efficiency of numerical software development. In A. M. Bruaset, E. Arge, and H. P. Langtangen, editors, Modern Software Tools for Scientific Computing. Birkhuser, 1997.Google Scholar
  2. 2.
    Diffpack website. http://www.diffpack.com.Google Scholar
  3. 3.
    H. P. Langtangen. Computational Partial Differential Equations-Numerical Methods and Diffpack Programming. Textbooks in Computational Science and Engineering. Springer, 2nd edition, 2003.Google Scholar
  4. 4.
    Donald W. Peaceman. Fundamentals of numerical reservoir simulations. Elsevier Scientific Publishing company, 1977.Google Scholar
  5. 5.
    Klas Samuelsson. Adaptive Algorithm for Finite Element Methods approximat-ing Flow Problems. PhD thesis, Royal Institute of Technology, Department of Numerical Analysis and Computing Science, Stockholm, Sweden, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Å. Ødegård
    • 1
  • H. P. Langtangen
    • 1
    • 2
  • A. Tveito
    • 1
    • 2
  1. 1.Simula Research LaboratoryNorway
  2. 2.Department of InformaticsUniversity of OsloNorway

Personalised recommendations