Bayliss, Alvin; Goldstein, Charles I.; Turkel, Eli An iterative method for the Helmholtz equation. (English) Zbl 0524.65068 J. Comput. Phys. 49, 443-457 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 87 Documents MSC: 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:preconditioned conjugate gradient methods; Helmholtz equation; numerical experiments; rate of convergence; symmetric successive overrelaxation; Laplace operator PDF BibTeX XML Cite \textit{A. Bayliss} et al., J. Comput. Phys. 49, 443--457 (1983; Zbl 0524.65068) Full Text: DOI OpenURL References: [1] Ahluwalia, D.S.; Keller, J.B., (), No. 20 [2] Axelsson, O., (), 2-51, No. 572 [3] Baumeister, K.J., Aiaa j., 18, 12, 1470, (1981) [4] Bayliss, A.; Gunzburger, M.D.; Turkel, E., SIAM J. appl. math., 47, 430, (1982) [5] Bayliss, A.; Turkel, E., Numerical boundary condition procedures, J. comput. phys., 48, 182, (1982) [6] Bowman, J.J.; Senior, T.B.A.; Uslenghi, P.L.E., Electromagnetic and acoustic scattering by simple bodies, (1969), North-Holland Amsterdam [7] Brandt, A., Math. comput., 31, 333, (1977) [8] Chandra, R., Conjugate gradient methods for partial differential equations, () [9] Concus, P.; Golub, G.H.; O’Leary, D.P., (), 309 [10] Ellman, H.C., () [11] Fix, G.J.; Marin, S., J. comput. phys., 28, 253, (1978) [12] Goldstein, C.I., Numer. math., 38, 61, (1981) [13] Goldstein, C.I., (), 307-313 [14] Goldstein, C.I., Math. comput., 39, (1982) [15] Hackbush, W., Math. comput., 34, 425, (1980) [16] Hestenes, M.R.; Stiefel, E., J. res. nat. bur. stand., 49, 409, (1952) [17] Kleinman, R.E.; Roach, G.F., SIAM rev., 16, 214, (1974) [18] Kriegsmann, G.A.; Morawetz, C.S., SIAM,. sci. statist. comput., 1, 371, (1980) [19] Kriegsmann, G.A., SIAM J. sci. statist. comput., 3, 318, (1982) [20] Lewis, R.M.; Keller, J.B., New York university report EM-194, (1964) [21] MacCamy, R.C.; Marin, S.P., Int. J. math. math. sci., 5, 311, (1980) [22] Nicolaides, R., Math. comput., 31, 892, (1977) [23] Nicolaides, R., Math. comput., 32, 1082, (1978) [24] Nodera, T.; Takahasi, H., Advances in computer methods for partial differential equations IV, (), 54-60 [25] Varga, R.S., Matrix iterative analysis, (1962), Prentice-Hall Englewood Cliffs, N. J · Zbl 0133.08602 [26] Widlund, O.B., SIAM J. numer. anal., 15, 801, (1978) [27] Young, D.M., Iterative solution of large linear systems, (1971), Academic Press New York · Zbl 0204.48102 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.