×

zbMATH — the first resource for mathematics

Relaxation schemes for spectral multigrid methods. (English) Zbl 0625.65112
Firstly this paper updates a paper of the author, T. A. Zang and M. Y. Hussaini [IMA J. Numer. Anal. 6, 273-292 (1986; Zbl 0624.65119)]. Two new forms of preconditioning by line relaxation are considered additionally, which were proposed for multigrid methods by A. Brandt [Math. Comput. 31, 333-390 (1977; Zbl 0373.65054)]. Numerical results for selfadjoint periodic elliptic problems are presented, which show, that incomplete LU decompositions are most effective in comparison with the other methods mentioned.
Reviewer: N.K√∂ckler

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brandt, A., Multi-level adaptive solutions to boundary-value problems, Math. comp., 31, 330-390, (1977) · Zbl 0373.65054
[2] Catherall, D., Optimum approximate factorization schemes for two-dimensional steady potential flows, Aiaa j., 20, 1057-1063, (1982) · Zbl 0511.76052
[3] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, 26, (1977), SIAM Philadelphia, PA, CBMS-NSF Regional Conference Series in Applied Mathematics · Zbl 0412.65058
[4] Haldenwang, P.; Labrosse, G.; Abboudi, S.; Deville, M., Chebyshev 3-D spectral and 2-D pseudospectral solvers for the Helmholtz equation, J. comput. phys., 55, 115-128, (1984) · Zbl 0544.65071
[5] Meijerink, J.A.; van der Vorst, H.A., Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems, J. comput. phys., 44, 134-155, (1981) · Zbl 0472.65028
[6] Orszag, S.A., Spectral methods for problems in complex geometries, J. comput. phys., 37, 70-92, (1980) · Zbl 0476.65078
[7] Phillips, T.N.; Zang, T.A.; Hussaini, M.Y., Preconditioners for the spectral multigrid method, IMA J. numer. anal., 6, 273-292, (1986), ICASE Report 83-48 · Zbl 0624.65119
[8] Street, C.L., A spectral method for the solution of transonic potential flow about an arbitrary airfoil, Proceedings of the sixth AIAA computational fluid dynamics conference, (1983), Danvers, MA, U.S.A.
[9] Streett, C.L.; Zang, T.A.; Hussaini, M.Y., Spectral multigrid methods with applications to transonic potential flow, J. comput. phys., 57, 43-76, (1985) · Zbl 0551.76053
[10] Wesseling, P., A robust and efficient multigrid method, (), Lecture Notes Math. · Zbl 0505.65052
[11] Wilkinson, J.H., The algebraic eigenvalue problem, (1965), Clarendon Press Oxford · Zbl 0258.65037
[12] Zang, T.A.; Wong, Y.S.; Hussaini, M.Y., Spectral multigrid methods for elliptic equations, J. comput. phys., 48, 485-501, (1982) · Zbl 0496.65061
[13] Zang, T.A.; Wong, Y.S.; Hussaini, M.Y., Spectral multigrid methods for elliptic equations II, J. comput. phys., 54, 489-507, (1984) · Zbl 0543.65071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.