Abstract
Spectral domain decomposition schemes are presented for the numerical solution of second and fourth order problems. These schemes, which are formulated in the collocation framework yield spectral approximations which are conforming along the subdomain interfaces for both conforming and non-conforming decompositions. For conforming decompositions the approximations are pointwise C 1 continuous across the interfaces for second order problems and C 3 continuous across the interfaces for fourth order problems. For non-conforming decompositions the corresponding approximations are pointwise C 0 and C1 continuous for second and fourth order problems, respectively. Efficient direct methods for the solution of the resulting systems are also presented.
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References
Karageorghis, A.: A fully conforming spectral collocation scheme for second and fourth order problems. Comp. Meth. Appl. Mech. Eng. 126 (1995) 305–314
Karageorghis, A., Sivaloganathan, S.: Conforming spectral approximations for nonconforming domain decompositions. Technical Report TR/07/96, Department of Mathematics and Statistics, University of Cyprus (1996)
Canuto, C., Hussaini, M., Quarteroni, A., Zang, T.: Spectral Methods in Fluid Dynamics. Springer-Verlag, New York (1988)
Boyd, J. P.: Chebyshev and Fourier Spectral Methods. Springer-Verlag, New York (1989)
Karageorghis, A., Paprzycki, M.: An efficient direct method for fully conforming spectral collocation schemes. Annals of Numerical Mathematics (to appear)
Karageorghis, A., Paprzycki, M.: Direct methods for spectral approximations in non-conforming domain decompositions.In preparation
UMFPACK, Versions 1.1 and 2.0, available from www.cis.ufl.edu∼davis
Numerical Algorithms Group Library Mark 15, NAG(UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK
Karageorghis, A., Phillips, T.N.: Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel. IMA Journal of Numer. Anal. 11 (1991) 33–54
Dennis, S.C.R., Smith, F.T.: Steady flow through a channel contraction with a symmetrical constriction in the form of a step. Proc. Roy. Soc. London A 372 (1980) 303–414
Paprzycki, M., Karageorghis, A.: High performance solution of linear systems arising from conforming spectral approximations for non-conforming domain decompositions. this volume
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© 1997 Springer-Verlag Berlin Heidelberg
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Karageorghis, A. (1997). Conforming spectral domain decomposition schemes. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_97
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DOI: https://doi.org/10.1007/3-540-62598-4_97
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