Skip to main content

The AGEB Algorithm for Solving the Heat Equation in Two Space Dimensions and Its Parallelization on a Distributed Memory Machine

  • Conference paper
Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 2003)

Abstract

In this paper, a computational analysis of parallelized a class of the AGE method based on the Brian variant (AGEB) is presented using (2 × 2) blocks. The resulting schemes are found to be effective in reducing data storage accesses and communication time on a distributed computer system. All the parallel strategies were developed on a cluster of workstations based on Parallel Virtual Machine environment [6]. The experiments were run on the homogeneous cluster of 20 Intel Pentium IV PCs, each with a storage of 20GB and speed of 1.6Mhz. Finally, the results of some computational experiments and performance measurements will be discussed. In conclusion, the communication cost and computational complexity have effected the efficiency of the parallel strategies.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Alias, N., Sahimi, M.S., Abdullah, A.R.: Parallel Algorithms On Some Numerical Techniques Using PVM Platform On A Cluster Of Workstations. In: Proceedings of the 7th Asian Technology Conference in Mathematics, vol. 7, pp. 390–397 (2002)

    Google Scholar 

  2. Alias, N., Sahimi, M.S., Abdullah, A.R.: Parallel Strategies For The Iterative lternating Decomposition Explicit Interpolation-Conjugate Gradient Method In solving Heat Conductor Equation On A Distributed Parallel Computer Systems. In: Proceedings of The 3rd International Conference on Numerical Analysis in Engineering, vol. 3, pp. 31–38 (2003)

    Google Scholar 

  3. Evans, D.J., Sahimi, M.S.: The Alternating Group Explicit Iterative Method (AGE) to Solve Parabolic and Hyperbolic Partial Differential Equations. In: Tien, C.L., Chawla, T.C. (eds.) Annual Review of Numerical Fluid Mechanics and Heat Transfer, vol. 2, Hemisphere Publication Corporation, New York (1989)

    Google Scholar 

  4. Evans, D.J., Sahimi, M.S.: The Alternating Group Explicit(AGE) Iterative Method for Solving Parabolic Equations I: 2-Dimensional Problems. Intern. J. Computer Math. 24, 311–341 (1988)

    Article  MATH  Google Scholar 

  5. Peaceman, D.W.: Fundamentals of Numerical Reservoir Simulation. Elsevier Scientific Publishing Company, Amsterdam (1977)

    Google Scholar 

  6. Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R., Sunderam, V.: PVM: Parallel Virtual Machine & User’s Guide and Tutorial for Networked Parallel Computing. MIT Press, Cambridge (1994)

    Google Scholar 

  7. Hwang, K., Xu, Z.: Scalable Parallel Computing: Technology, Architecture, Programming. McGraw-Hill, New York (1998)

    MATH  Google Scholar 

  8. Lewis, T.G., EL-Rewini, H.: Distributed and Parallel Computing. Manning Publication, USA (1998)

    Google Scholar 

  9. Wilkinson, B., Allen, M.: Parallel Programming Techniques and Applications Using Networked Workstations and Parallel Computers. Prentice Hall, Upper Saddle River (1999)

    Google Scholar 

  10. Zamoya, A.Y.: Parallel and Distribution Computing Handbook. McGraw-Hill, New York (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alias, N., Sahimi, M.S., Abdullah, A.R. (2003). The AGEB Algorithm for Solving the Heat Equation in Two Space Dimensions and Its Parallelization on a Distributed Memory Machine. In: Dongarra, J., Laforenza, D., Orlando, S. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2003. Lecture Notes in Computer Science, vol 2840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39924-7_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-39924-7_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20149-6

  • Online ISBN: 978-3-540-39924-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics