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.
This paper reports results of a research projekt supported by the DFG Schwerpunktprogram “Finite Approximationen in der Strömungsmechanik”)
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References
BALLMANN,J, EPPLER,R. and HACKBUSCH,W.(eds): Panel Methods in Mechanics. To appear in the series “Notes on numerical fluid mechanics”; Vieweg, Braunschweig 1987
HACKBUSCH,W.: Multi-grid methods and applications. Springer, Berlin 1985
HACKBUSCH,W.: Theorie und Numerik elliptischer Differentialgleichungen. Teubner, Stuttgart 1986
HACKBUSCH,W. and NOWAK,Z.P.: Multi-grid methods for calculating the lifting potential incompressible flows around three-dimensional bodies. In [7] 135–148
HACKBUSCH,W. and NOWAK,Z.P.: A multi-level discretisation and solution method for potential flow problems in three dimensions. In [8]
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 1986
HACKBUSCH,W. and TROTTENBERG,U.(eds): Multi-grid methods II. Proceedings, Köln, Oct. 1985. Lecture Notes in Math 1228. Springer, Berlin 1986
HIRSCHEL,E.H.(ed): Finite approximation in fluid mechanics. Notes on Numerical Fluid Mechanics 14. Vieweg, Braunschweig 1986
JASWON,M.A. and SYMM,G.T: Integral equation methods in potential theory and elastostatics. Academic Press, London 1977
NOWAK,Z.P.: A new type of higher-order boundary integral approximation for potential flow in three dimensions. In [8]
NOWAK,Z.P.: Panel clustering technique for lifting potential flows in the three space dimensions. In [1]
NOWAK,Z.P.: Report, Universität Kiel, to appear in 1987
ROKHLIN,V.: Rapid solution of integral equations of classical potential theory. J. Comp. Physics 60 (1985) 187–207
HACKBUSCH,W. and NOWAK,Z.P.: On the fast matrix multiplication in the boundary element method by panel clustering. To appear.
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© 1987 Springer-Verlag Berlin Heidelberg
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Hackbusch, W. (1987). The Panel Clustering Technique for the Boundary Element Method (Invited contribution) . In: Brebbia, C.A., Wendland, W.L., Kuhn, G. (eds) Mathematical and Computational Aspects. Boundary Elements IX, vol 9/1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21908-9_30
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DOI: https://doi.org/10.1007/978-3-662-21908-9_30
Publisher Name: Springer, Berlin, Heidelberg
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