Advertisement

The Panel Clustering Technique for the Boundary Element Method (Invited contribution)

  • W. Hackbusch
Part of the Boundary Elements IX book series (BOUNDARY, volume 9/1)

Summary

In contrast to usual finite element methods the boundary element method leads to systems with full matrices. This fact seems to require much computational work for the definition of the matrix entries, for the solution of the system, and, in particular, for the matrix-vector multiplication, which always occurs as an elementary operation. In this paper a method for the approximate matrix-vector multiplication is described which requires much less arithmetical work. In addition, the storage requirements are strongly reduced.

Keywords

Boundary Element Boundary Element Method Collocation Point Computational Aspect Panel Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BALLMANN,J, EPPLER,R. and HACKBUSCH,W.(eds): Panel Methods in Mechanics. To appear in the series “Notes on numerical fluid mechanics”; Vieweg, Braunschweig 1987Google Scholar
  2. [2]
    HACKBUSCH,W.: Multi-grid methods and applications. Springer, Berlin 1985MATHCrossRefGoogle Scholar
  3. [3]
    HACKBUSCH,W.: Theorie und Numerik elliptischer Differentialgleichungen. Teubner, Stuttgart 1986MATHCrossRefGoogle Scholar
  4. [4]
    HACKBUSCH,W. and NOWAK,Z.P.: Multi-grid methods for calculating the lifting potential incompressible flows around three-dimensional bodies. In [7] 135–148Google Scholar
  5. [5]
    HACKBUSCH,W. and NOWAK,Z.P.: A multi-level discretisation and solution method for potential flow problems in three dimensions. In [8]Google Scholar
  6. [6]
    HACKBUSCH,W. and NOWAK,Z.P.: On the complexity of the panel method (in Russ.). To appear in the proceedings of the conference “Modern Problems in Numerical Analysis”, Moscow, Sept 1986 Also in Report 8608, Universität Kiel, Sept 1986Google Scholar
  7. [7]
    HACKBUSCH,W. and TROTTENBERG,U.(eds): Multi-grid methods II. Proceedings, Köln, Oct. 1985. Lecture Notes in Math 1228. Springer, Berlin 1986Google Scholar
  8. [8]
    HIRSCHEL,E.H.(ed): Finite approximation in fluid mechanics. Notes on Numerical Fluid Mechanics 14. Vieweg, Braunschweig 1986Google Scholar
  9. [9]
    JASWON,M.A. and SYMM,G.T: Integral equation methods in potential theory and elastostatics. Academic Press, London 1977MATHGoogle Scholar
  10. [10]
    NOWAK,Z.P.: A new type of higher-order boundary integral approximation for potential flow in three dimensions. In [8]Google Scholar
  11. [11]
    NOWAK,Z.P.: Panel clustering technique for lifting potential flows in the three space dimensions. In [1]Google Scholar
  12. [12]
    NOWAK,Z.P.: Report, Universität Kiel, to appear in 1987Google Scholar
  13. [13]
    ROKHLIN,V.: Rapid solution of integral equations of classical potential theory. J. Comp. Physics 60 (1985) 187–207MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    HACKBUSCH,W. and NOWAK,Z.P.: On the fast matrix multiplication in the boundary element method by panel clustering. To appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • W. Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische Mathematik Christian-Albrechts-Universität KielKiel 1Germany

Personalised recommendations