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Title: Spectral methods for singular perturbation problems (English)
Author: Heinrichs, Wilhelm
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 39
Issue: 3
Year: 1994
Pages: 161-188
Summary lang: English
Category: math
Summary: We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented. (English)
Keyword: spectral methods
Keyword: singular perturbation
Keyword: stabilization
Keyword: domain decomposition
Keyword: iterative solver
Keyword: multigrid method
MSC: 35B25
MSC: 35J25
MSC: 65F10
MSC: 65N12
MSC: 65N35
MSC: 65N55
idZBL: Zbl 0812.65100
idMR: MR1273631
DOI: 10.21136/AM.1994.134251
Date available: 2009-09-22T17:43:38Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] C. Canuto: Spectral methods and maximum principle, to appear in Math. Comp... MR 0930226
Reference: [2] C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang: Spectral methods in fluid dynamics.Springer-Verlag, New York-Berlin-Heidelberg, 1988. MR 0917480
Reference: [3] J. Doerfer: Mehrgitterverfahren bei singulaeren Stoerungen.Master Thesis, Duesseldorf, 1986.
Reference: [4] J. Doerfer and K. Witsch: Stable second order discretization of singular perturbation problems using a hybrid technique.(to appear).
Reference: [5] D. Funaro: Computing with spectral matrices.(to appear).
Reference: [6] D. Funaro, A. Quarteroni and P. Zanolli: An iterative procedure with interface relaxation for domain decomposition methods.SIAM J. Num. Anal. 25 (1988). MR 0972451, 10.1137/0725069
Reference: [7] W. Hackbusch: Theorie und Numerik elliptischer Differentialgleichungen.Teubner Studienbücher, Stuttgart, 1986. Zbl 0609.65065, MR 1600003
Reference: [8] W. Heinrichs: Line relaxation for spectral multigrid methods.J. Comp. Phys. 77 (1988), 166–182. Zbl 0649.65055, MR 0954308, 10.1016/0021-9991(88)90161-1
Reference: [9] W. Heinrichs: Multigrid methods for combined finite difference and Fourier problems.J. Comp. Phys. 78 (1988), 424–436. Zbl 0657.65118, MR 0965660, 10.1016/0021-9991(88)90058-7
Reference: [10] T. Meis, U. Markowitz: Numerische Behandlung partieller Differentialgleichungen.Springer-Verlag, Berlin-Heidelberg-New York, 1978. MR 0513829
Reference: [11] S.A. Orszag: Spectral methods in complex geometries.J. Comp. Phys. 37 (1980), 70–92. MR 0584322, 10.1016/0021-9991(80)90005-4
Reference: [12] H. Yserentant: Die Mehrstellenformeln für den Laplaceoperator.Num. Math. 34 (1980), 171–187. MR 0566680, 10.1007/BF01396058
Reference: [13] T.A. Zang, Y.S. Wong and M.Y. Hussaini: Spectral multigrid methods for elliptic equations I.J. Comp. Phys. 48 (1982), 485–501. MR 0755459, 10.1016/0021-9991(82)90063-8
Reference: [14] T.A. Zang, Y.S. Wong and M.Y. Hussaini: Spectral multigrid methods for elliptic equations II.J. Comp. Phys. 54 (1984), 489–507. MR 0755456, 10.1016/0021-9991(84)90129-3


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