Skip to main content
SpringerLink
Log in
Book cover

Boundary Elements: Implementation and Analysis of Advanced Algorithms pp 171–181Cite as

Parallel Setup of Galerkin Equation System for a Geodetic Boundary Value Problem

  • Chapter

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM,volume 50))

Summary

A particular problem in setting up large Galerkin equation systems in the 3D-BEM is the huge number of offdiagonal elements, which are mainly regular integrals over pairs of boundary elements. The numerical effort of cubature depends strongly on the distance between these elements. Therefore, the polynomial degree of exactness of the cubature formula may be chosen based on an estimate of the distance. In a straightforward implementation on a parallel computer, this may lead to severe imbalances of workload, which considerably reduces the speedup. To overcome this difficulty, a dynamic load balancing scheme is applied. It is shown how this works in the solution of the classical oblique boundary value problem (BVP) of potential theory (which results from the linearization of the fixed BVP of Physical Geodesy) on a IBM 9076 SP/2.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ANDRÄ, H. (1995): GBEMINT Version 1.03g. Kurzanleitung. Inst. f. Mechanik und Festigkeitslehre, Universität Karlsruhe (TH).

    Google Scholar 

  2. BROVAR, V.V. (1963): Solutions of the Molodenskij boundary problem. Geodesy and Aerophotography, 237–240.

    Google Scholar 

  3. BROVAR, V.V. (1964): Fundamental harmonic functions with a singularity on a segment and solution of outer boundary problems. Geodesy and Aerophotography, 150–155.

    Google Scholar 

  4. GIRAUD, G. (1934): Equations integrales principales. Annales Scientifiques de l’Ecole Normale Superieure, Troisieme Serie, 51: 251–372.

    MATH  Google Scholar 

  5. HERZIG, TH. (1994): Ein paralleles 3D-Randelementprogramm der Elektrostatik für heterogene Rechnerarchitekturen. Dissertation. Universität Karlsruhe (TH).

    Google Scholar 

  6. INGBER, M.S., D.E. WOMBLE, L.A. MONDY (1994): A Parallel Boundary Element Formulation for Determining Effective Properties of Heterogeneous Media. Int. J. Num. Meth. Eng. 37, 3905–3920.

    Google Scholar 

  7. JOHNSON, C.G.L., L.R. SCOTT (1989): An Analysis of Quadrature Errors in Second Kind Boundary Integral Equations. SIAM, J. of Numer. Anal. 16 1356–1382.

    Article  MathSciNet  Google Scholar 

  8. KLEES, R. (1992): Lösung des fixen geodätischen Randwertproblems mit Hilfe der Randelementmethode. Veröffentl. d. Dt. Geod. Kommiss. b. d. Bayer. Akad. d. Wiss., Reihe C, Heft Nr. 382, München.

    MATH  Google Scholar 

  9. KROMMER, A.R., C.W. UEBERHUBER (1994): Numerical Integration on Advanced Computer Systems. Lecture Notes in Computer Sciences, Vol. 848. Springer Verlag Berlin Heidelberg.

    Book  Google Scholar 

  10. LYNESS, J.N., D. JESPERSON (1975): Moderate degree symmetric quadrature rules for the triangle. J. Inst. Math. Appl. 15, 19–32.

    Article  MathSciNet  MATH  Google Scholar 

  11. SAUTER, S.A. (1992): Über die effiziente Verwendung des Galerkin-Verfahrens zur Lösung Fredholmscher Integralgleichungen. Dissertation. Christian-Albrechts-Universität Kiel.

    Google Scholar 

  12. SAUTER, S.A., A. KRAPP (1995): On the Effect of Numerical Integration in the Galerkin Boundary Element Method. Inst. f. Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Report No. 9504.

    Google Scholar 

  13. SCHWAB, Chr., WENDLAND, W.L. (1992): Kernel properties and representations of boundary integral operators. Math. Nachr. 156: 187–218.

    Article  MathSciNet  MATH  Google Scholar 

  14. WENDLAND, W.L. (1990): Boundary element methods for elliptic problems. In: A.H. Schatz, V. Thomee, W.L. Wendland, “Mathematical Theory of Finite and Boundary Element Methods”, DMV Seminar Vol. 15, Birkhaeuser: 223–276.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Geodetic Institute, University of Karlsruhe, Englerstr. 7, D-76128, Karlsruhe, Germany

    Rüdiger Lehmann

  2. Faculty of Geodetic Engineering, Delft University of Technology, Thijsseweg 11, NL-2629 JA, Delft, The Netherlands

    Roland Klees

Authors
  1. Rüdiger Lehmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roland Klees
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Lehrstuhl Praktische Mathematik, Mathematisches Seminar II, Christian-Albrechts-Universität Kiel, Hermann-Rodewald-Str. 3, 24098, Kiel, Germany

    Wolfgang Hackbusch

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

About this chapter

Cite this chapter

Lehmann, R., Klees, R. (1996). Parallel Setup of Galerkin Equation System for a Geodetic Boundary Value Problem. In: Hackbusch, W., Wittum, G. (eds) Boundary Elements: Implementation and Analysis of Advanced Algorithms. Notes on Numerical Fluid Mechanics (NNFM), vol 50. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89941-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-89941-5_14

  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-322-89943-9

  • Online ISBN: 978-3-322-89941-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation