Skip to main content
SpringerLink
Log in

A Parallel ADI and Steepest Descent Methods

  • Conference paper
  • First Online:
Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2131))

  • 504 Accesses

Abstract

The aim of the paper is an improvement of a parallel alternating-direction implicit, or ADI, method for solving the two-dimensional equation of ground water flow and its implementation on a distributedmemory MIMD-computer under the MPI message-passing system. Besides, the paper represents evaluation of the parallel algorithm in terms of relative efficiency and speedup. The obtained results show that for reasonably large discretization grids the parallel ADI method is effective enough on a large number of processors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J.M., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., Henk Van der Vorst: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, http://www.netlib.org/templates/Templates.html

  2. Bear, J., Zaslavsky, D., Irmay, S.: Physical principles of water percolation and seepage. UNESCO, (1968)

    Google Scholar 

  3. Foster, I.: Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering, Addison-Wesley Pub. Co., (1995)

    Google Scholar 

  4. Gropp, W., Lusk, E., Skjellum, A., Rajeev, T.: Using MPI: Portable Parallel Programming With the Message-Passing Interface, Mit press, (1999)

    Google Scholar 

  5. Krukier L.A., Schevtschenko I.V.: Modeling Gravitational Flow of Ground Water. Proceedings of the Eighth All-Russian Conference on Modern Problems of Mathematical Modeling, Durso, Russia, September 6–12, RSU Press, (1999), 125–130

    Google Scholar 

  6. MPI: A Message-Passing Interface Standard, Message Passing Interface Forum, (1994)

    Google Scholar 

  7. Pacheco, P.: Parallel Programming With MPI, Morgan Kaufamnn Publishers, (1996)

    Google Scholar 

  8. Peaceman, D., and Rachford, J. H.H.: The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math., No. 3 (1955), 28–41

    Google Scholar 

  9. Samarskii, A.A., and Goolin, A.V.: Numerical Methods, Main Editorial Bord for Physical and Mathematical Literature, (1989)

    Google Scholar 

  10. Wallach, Y.: Alternating Sequential/Parallel Processing, Springer-Verlag, (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Computational Experiments on Super Computers, Rostov State University, Zorge street 5, Rostov-on-Don, 344090, Russia

    I. V. Schevtschenko

Authors
  1. I. V. Schevtschenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Informatics and Telecommunications, University of Athens, Panepistimiopolis, 157 84, Greece

    Yiannis Cotronis

  2. Innovative Computing Lab., Computer Science Department, University of Tennessee, 1122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schevtschenko, I.V. (2001). A Parallel ADI and Steepest Descent Methods. In: Cotronis, Y., Dongarra, J. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2001. Lecture Notes in Computer Science, vol 2131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45417-9_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-45417-9_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42609-7

  • Online ISBN: 978-3-540-45417-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation