Skip to main content
SpringerLink
Log in

Hyper-Rectangle Distribution Algorithm for Parallel Multidimensional Numerical Integration

  • Conference paper
  • First Online:
Book cover Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1697))

Abstract

In this paper we consider parallel numerical integration algorithms for multi-dimensional integrals. A modified algorithm of hyper-rectangle selection and distribution strategy is proposed for the implementation of globally adaptive parallel quadrature algorithms. A list of subproblems is distributed among slave processors. Numerical results on the SP2 computer and on a cluster of workstations are reported. A test problem where the integrand function has a strong corner singularity is investigated.

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. Bull, J.M., Freeman, T.L.: Parallel Globally Adaptive Algorithms for Multi-dimensional Integration. Applied Numerical Mathematics 19 (1995) 3–16

    Article  MATH  Google Scholar 

  2. Freeman T.L. and Phillips C.: Parallel Numerical Algorithms. Prentice Hall, New York, London, Toronto, Sydney, Tokyo, Singapore (1991).

    Google Scholar 

  3. Čiegis, R., Šablinskas, R., Waśniewski, J.: Numerical Integration on Distributed Memory Parallel Systems. In: Bubak, M., Dongarra, J., Waśniewski, J. (eds.): Recent Advances in PVM and MPI. Lecture Notes in Computer Science, Vol. 1332. Springer-Verlag, Berlin Heidelberg New York (1997) 329–336

    Google Scholar 

  4. Čiegis, R., Šablinskas, R., Waśniewski J.: Hyper-rectangle selection strategy for parallel adaptive numerical integration. In: B. Kagstrom, Dongarra, J., Elmroth, E., Waśniewski, J. (eds.): Proc. 4th International Workshop PARA98. Lecture Notes in Computer Science, Vol. 1541. Springer-Verlag, Berlin Heidelberg New York (1998) 71–75

    Google Scholar 

  5. Genz, A.C., Malik, A.A.: Remarks on Algorithm 006: an Adaptive Algorithm for Numerical Integration Over an N-dimensional Rectangular Region. J. Comput. Appl. Math. 6 (1980) 295–302

    Article  MATH  Google Scholar 

  6. Keister, B.D.: Multi-dimensional Quadrature Algorithms. Computers in Physics, 10 (1996) 119–122

    Article  Google Scholar 

  7. Miller, V.A., Davis, G.J.: Adaptive Quadrature on a Message Passing Multi-processor. J. Parallel Distributed Comput., 14 (1992) 417–425

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, LT-2600, Vilnius, Lithuania

    Raimondas Čiegis

  2. Vilnius Gediminas Technical University, Saulètekio 11, LT-2054, Vilnius, Lithuania

    Raimondas Čiegis & Ramūnas Šablinskas

  3. Vytautas Magnus University, Vileikos 8, 3035, Kaunas, Lithuania

    Ramūnas Šablinskas

  4. The Danish Computing Centre for Research and Education, UNI-C, Bldg. 305, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

Authors
  1. Raimondas Čiegis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramūnas Šablinskas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jerzy Waśniewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. OakRidge National Laboratory, University of Tennessee, 107, Ayres Hall, Knoxville, TN, 37996-1301, USA

    Jack Dongarra

  2. Computer Science Department Computer Architecture and Operating Systems Group, Universitat Autònoma of Barcelona, E-08193, Bellaterra, Barcelona, Spain

    Emilio Luque  & Tomàs Margalef  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Čiegis, R., Šablinskas, R., Waśniewski, J. (1999). Hyper-Rectangle Distribution Algorithm for Parallel Multidimensional Numerical Integration. In: Dongarra, J., Luque, E., Margalef, T. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 1999. Lecture Notes in Computer Science, vol 1697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48158-3_34

Download citation

  • DOI: https://doi.org/10.1007/3-540-48158-3_34

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66549-6

  • Online ISBN: 978-3-540-48158-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation