×

zbMATH — the first resource for mathematics

Boundary and interface conditions within a finite element preconditioner for spectral methods. (English) Zbl 0717.65091
Authors’ summary: The performances of a finite element preconditioner in the iterative solution of spectral collocation schemes for elliptic boundary value problems is investigated. It is shown how to make the preconditioner cheap by ADI iterations and how to take advantage of the finite element properties in enforcing Neumann and interface conditions in the spectral schemes.
Reviewer: W.Ames

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
65F35 Numerical computation of matrix norms, conditioning, scaling
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Canuto, C., Parallelism in spectral methods, () · Zbl 0675.65117
[2] Canuto, C.; Hussaini, M.H.; Quarteroni, A.; Zang, T.A., Spectral methods in fluid dynamics, (1988), Springer-Verlag New York · Zbl 0658.76001
[3] Canuto, C.; Quarteroni, A., J. comput. phys., 60, 315, (1985)
[4] Douglas, C., Numer. math., 4, 41, (1962)
[5] Douglas, J.; Dupont, T., Alternating-direction Galerkin methods on rectangles, (), 133
[6] Deville, M.; Mund, E., J. comput. phys., 60, 517, (1985)
[7] Dihn, Q.V.; Glowinski, R.; Periaux, J., Solving elliptic systems by domain decomposition methods with applications, (), 395 · Zbl 0575.65096
[8] Funaro, D., (), (unpublished)
[9] Hayes, L.J., SIAM J. numer. anal., 18, 627, (1981)
[10] Haldenwang, P.; Labrosse, G.; Abboudi, S.; Deville, M., J. comput. phys., 55, 115, (1984)
[11] Marion, Y.; Gay, B., Resolution des equations de Navier-Stokes par methode pseudo-spectrale via une technique de coordination, ()
[12] Orszag, S.A., J. comput. phys., 37, 70, (1980)
[13] Peaceman, D.W.; Rachford, H.H., SIAM J. numer. anal., 3, 28, (1955)
[14] Wong, Y.S.; Zang, T.A.; Hussaini, M.Y., Comput. fluids, 14, 85, (1986)
[15] Bayliss, A.; Matkowsky, B., J. comput. phys., 71, 147, (1987)
[16] Bayliss, A.; Gottlieb, D.; Matkowsky, B.; Minkoff, M., J. comput. phys., 81, 421, (1989)
[17] \scM. Deville and E. Mund“Finite Element Preconditioning for Pseudospectral Solutions of Elliptic Problems,” manuscript in preparation. · Zbl 0701.65075
[18] Yanenko, N.N., The method of fractional steps, (1971), Springer-Verlag Berlin · Zbl 0209.47103
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.