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A multigrid method for the generalized symmetric eigenvalue problem. I: Algorithm and implementation. (English) Zbl 0775.73340


MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74H45 Vibrations in dynamical problems in solid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
Full Text: DOI

References:

[1] ABAQUS Version 4-6, Hibbitt, Karlsson, and Sorenson, Inc.
[2] and , Finite Element Solution of Boundary Value Problems, Academic Press, New York, 1984.
[3] , , and , ’Multigrid methods for linear elastic stress problems’, in and (eds.), Multigrid Methods for Integral and Differential Equations Clarendon Press, Oxford, 1985, pp. 263-282.
[4] Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1982.
[5] Belytschko, Comp. Methods Appl. Mech. Eng. 29 pp 313– (1981)
[6] Bradbury, Numerische Mathematik 9 pp 259– (1966)
[7] Braess, Comp. Mech. 3 pp 321– (1988)
[8] Brandt, Math. Comp. 31 pp 333– (1977)
[9] Hackbusch, SIAM J. Numer. Anal. 16 pp 201– (1979)
[10] Multi-Grid Methods and Applications, Springer-Verlag, Berlin, 1985. · Zbl 0595.65106 · doi:10.1007/978-3-662-02427-0
[11] Hestenes, J. Res. Nat. Bur. Standards 47 pp 45– (1951) · doi:10.6028/jres.047.008
[12] and , ’Large-scale vectorized implicit calculations is solid mechanics on CRAYX-MP/48 utilizing EBE preconditioned conjugate gradients’, in (ed.), Computational Mechanics–Advances and Trends, ASME, New York, 1986, pp. 233-277.
[13] Hwang, Int. j. numer. methods eng. 35 pp 1677– (1992)
[14] Kosloff, Int. j. numer. anal. methods geomech. 2 pp 57– (1978)
[15] Papadrakakia, Comp. Methods Appl. Mech. Eng. 62 pp 195– (1987)
[16] Parsons, Comp. Phys. Commun. 53 pp 337– (1989)
[17] Parsons, Int. j. numer. methods eng. 29 pp 719– (1990)
[18] Parsons, Int. j. numer. methods eng. 29 pp 739– (1990)
[19] and , ’Multigrid methods: Fundamental algorithms, model problem analysis and applications’, in and (eds.), Multigrid Methods, Springer-Verlag, Berlin, 1982, pp. 1-176.
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