Skip to main content
SpringerLink
Log in

The Effect of Essential Boundary Conditions on the Convergence of Iterative Equation Solvers in BEM

  • Conference paper
Computational Mechanics ’95

  • 21 Accesses

Abstract

This paper first examines the spectral properties of the matrix equations generated from BEM in two-dimensional potential and elasticity theories. This paper then shows that as the number of essential boundary conditions is increased, Jacobia and Gauss-Seidel iterative equation solvers in general will not converge for the BEM system of equations. The reason why these solvers do not converge is due to the presence of the G influence matrix terms in the coefficient matrix A.

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 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.

Similar content being viewed by others

References

  1. Brebbia, C. A. and Dominguez, J., Boundary Elements: An Introductory Course, Co-published by Computational Mechanics Publications, Southampton and McGraw-Hill, New York, p. 216 & p. 54 (1992).

    MATH  Google Scholar 

  2. Golub, G. H. and Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, pp. 52–81 (1983).

    MATH  Google Scholar 

  3. Smith, B. T., Boyle, J. M., Dongerra, J. J., Garbow, B. S., Ikebe, Y., Klema, V. C. and Moler, C. B., ‘Matrix Eigensystems Routines — EISPACK Guide,’ Lecturer Notes in Computer Science, Vol. 6, Springer-Verlag, Heidelberg (1976).

    Book  Google Scholar 

  4. Urekew, T. J. and Rencis, J. J., “An Iterative Solution Strategy for Boundary Element Equations from Mixed Boundary Value Problems,” Computer Methods in Applied Mechanics and Engineering, 118, 13–28 (1994).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Dept., Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Joseph J. Rencis

  2. Thermo Electron Web Systems, Inc., P.O. Box 269, 35 Sword Street, Auburn, MA, USA

    Kimberly C. Mann

  3. Kulicke and Soffa Industries, 2101 Blairmill Road, Willow Grove, PA, 19090, USA

    Timothy J. Urekew

Authors
  1. Joseph J. Rencis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kimberly C. Mann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Timothy J. Urekew
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computational Modeling Center, Georgia Institute of Technology, Atlanta, GA, 30332-0356, USA

    S. N. Atluri

  2. Department of Quantum Engineering & Systems Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan

    G. Yagawa

  3. Department of Mechanical Engineering, Vanderbilt University, P.O. Box 1592, Station B, Nashville, TN, 37235, USA

    Thomas Cruse

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rencis, J.J., Mann, K.C., Urekew, T.J. (1995). The Effect of Essential Boundary Conditions on the Convergence of Iterative Equation Solvers in BEM. In: Atluri, S.N., Yagawa, G., Cruse, T. (eds) Computational Mechanics ’95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79654-8_446

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-79654-8_446

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-79656-2

  • Online ISBN: 978-3-642-79654-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation