Abstract
Recently, boundary element methods have found dramatically increasing interest for the numerical treatment of a large variety of problems arising in the engineering sciences (e.g. Brebbia et al.3). They serve as highly efficient but slightly specialized numerical methods. Hence a strong line of research is to combine boundary element methods with other well experienced methods in order to optimize their specific (often complementary) advantages. This has been successfully done mixing boundary elements and finite elements (Zienkiewicz, Kelly and Bettess13; Johnson and Nedelec9; Wendland12; Hsiao and Porter8). A different combination which seems to be even more advantageous under certain circumstances is that of boundary elements and fast spectral methods (Hebeker6; Borchers, Hebeker and Rautmann2). This hybrid approach, called boundary element spectral method, is briefly described in the present note.
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References
Borchers, W. (1985), Eine Fourier-Spektralmethode für das Stokes Resolventenproblem. Preprint U. of Paderborn, 13 pp., submitted.
Borchers, W., Hebeker, F.K., and Rautmann, R. (1985), A Boundary Element Spectral Method for Nonstationary Viscous Flows in Three Dimensions. In: Finite Approximationen in der Strömungsmechanik (Ed. Hirschel E.H.), pp. 14–28, Vieweg, Braunschweig.
Brebbia, C.A. et al. (ed.) (1985), Boundary Element Methods in Engineering. Proc. 7th Intl. Conf. on BEM., Como, Italy, 1985. Springer, Berlin.
Hebeker, F.K. (1985), Efficient Boundary Element Methods for 3-D Viscous Flows. Numerical Methods in PDE, 35 pp., in press.
Hebeker, F.K. (1985), Efficient Boundary Element Methods for 3-D Viscous Flows. In: Brebbia3, pp. 9: 37–44.
Hebeker, F.K. (1986), On a New Boundary Element Spectral Method. In: Innovative Numerical Methods in Engineering (Ed. Shaw R.P. et al.), pp. 311–316, Proc. of 4th Intl. Symp., Atlanta Ga., USA., 1986. Springer, Berlin.
Hebeker, F.K. (1986), On the Numerical Treatment of Viscous Flows Past Bodies with Corners and Edges. In: Efficient Numerical Methods in Continuum Mechanics (Ed. Hackbusch W.), 6 pp., Proc. GAMM Seminar, Kiel, West Germany, 1986, in press. Vieweg, Braunschweig.
Hsiao G.C. and Porter J.F. (1986), A Hybrid Method for an Exterior Boundary Value Problem Based on Asymptotic Expansion, Boundary Integral Equation and Finite Element Approximation. In: Innovative Numerical Methods in Engineering (see Hebeker6), pp. 83–88.
Johnson C. and Nedelec J.C. (1980), On the Coupling of Boundary Integral and Finite Element Methods. Math. Comp., Vol. 35, pp. 1063–1079.
Varnhorn, W. (1985), Zur Numerik der Gleichungen von Navier-Stokes. PhD Thesis, U. of Paderborn.
Wendland, W.L. (1985), On Some Mathematical Aspects of Boundary Element Methods for Elliptic Problems. In: The Mathematics of Finite Elements and Applications V (Ed. Whiteman J.R.), pp. 193–227.
Wendland, W.L. (1986), On Asymptotic Error Estimates for the Combined Boundary and Finite Element Method. In: Innovative Numerical Methods in Engineering (see Hebeker6), pp. 55–69.
Zienkiewicz, O.C., Kelly D.W. and Bettess, B. (1977), The Coupling of the Finite Element Method and Boundary Solution Procedures. Intl. J. Num. Meth. Engin., Vol. 11, pp. 355–375.
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Borchers, W., Hebeker, F.K. (1986). The Boundary Element Spectral Method and Applications in 3-D Viscous Hydrodynamics. In: Tanaka, M., Brebbia, C.A. (eds) Boundary Elements VIII. Boundary Elements, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22335-2_28
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