Multigrid preconditioner for unstructured nonlinear 3D FE models

Journal of Engineering Mechanics

Volumn 125, Issue 2, 1999, Pages 186-196

  Davids, William G ^a   Turkiyyah, George M ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENDING (DEFORMATION); COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; INTEGRATION; INTERPOLATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PROBLEM SOLVING; STIFFNESS MATRIX;

CONJUGATE-GRADIENT SOLUTION; MULTIGRID METHODS; NODAL CONTACT NONLINEARITY;

PAVEMENTS;

EID: 0033076196     PISSN: 07339399     EISSN: None     Source Type: Journal    
DOI: 10.1061/(ASCE)0733-9399(1999)125:2(186)     Document Type: Article

References (26)

1. Ashby, S., and Falgout, R. (1996). "A parallel multigrid preconditioned conjugate gradient algorithm for groundwater flow simulations." Nuclear Sci. and Engrg., 124, 145-159.
2. Bathe, K.-J. (1996). Finite element procedures. Prentice-Hall, Englewood Cliffs, N.J.
3. Brandt, A. (1977). Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation, 31(138), 333-390.
4. Channakeshava, C., Barzegar, F., and Voyiadjis, G. (1993). "Nonlinear FE analysis of plain concrete pavement with doweled joints." J. Transp. Engrg., 119(5), 763-781.
5. Darter, M., Hall, K., and Kuo, C.-M. (1995). "Support under Portland cement concrete pavements." NCHRP report No. 372 National Cooperative Highway Research Program, Washington, D.C.
6. Davids, W., and Turkiyyah, G. (1997). "Development of embedded bending member to model dowel action." J. Struct. Engrg., 123(10), 1312-1320.
7. Demmel, J. W., Gilbert, J. R., and Li, X. S. (1997). SuperLU users' guide. Comp. Sci. Div., University of California, Berkeley, Berkeley, Calif.
8. Dracopoulos, M., and Crisfield, M. (1995). "Coarse/fine mesh preconditioners for the iterative solution of finite element problems." Int. J. Numer. Methods in Engrg., 38, 3297-3313.
9. Farhat, C., and Sobh, N. (1989). "A coarse/fine mesh preconditioner for very ill-conditioned finite element problems." Int. J. Numer. Methods in Engrg., 28, 1715-1723.
10. Fish, J., Pan, L., Belsky, V., and Gomaa, S. (1996). "Unstructured multigrid method for shells." Int. J. Numer. Methods in Engrg., 39, 1181-1197.
11. Goodman, J. E., and O'Rourke, J. (1997). Handbook of discrete and computational geometry. CRC, Boca Raton, Fla.
12. Jesperson, D. (1984). "Multigrid methods for partial differential equations." MAA studies in mathematics, G. Golub, ed., Vol. 24, Mathematical Assoc. of America, Washington, D.C., 270-317.
13. Kǒcvara, M. (1993). "An adaptive multigrid technique for three-dimensional elasticity." Int. J. Numer. Methods in Engrg., 36, 1703-1716.
14. Kuo, C.-M., Hall, K., and Darter, M. (1996). "Three-dimensional finite element model for analysis of concrete pavement support." Transp. Res. Rec. 1505, TRB, National Research Council, Washington, D.C., 119-127.
15. Li, X. S. (1996). Sparse Gaussian elimination on high performance computers. Comp. Sci. Div., University of California, Berkeley, Berkeley, Calif.
16. Löhner, R., and Morgan, K. (1987). "An unstructured multigrid method for elliptic problems." Int. J. Numer. Methods in Engrg., 24, 101-115.
17. Meza, J., and Tuminaro, R. (1996). "A multigrid preconditioner for the semiconductor equations." SIAM J., 17(1), 118-132.
18. Mitchell, S., and Vavasis, S. (1992). "Quality mesh generation in three dimensions." Proc., ACM Computational Geometry Conf., Assoc. for Computing Machinery, New York, 212-221.
19. Muttin, F., and Chenot, J.-L. (1995). "On a conjugate-gradient two-grid method for three-dimensional elasticity." Engrg. Computations, 12, 3-20.
20. Oosterlee, C., and Washio, Y. (1998). An evaluation of parallel multigrid as a solver and a preconditioner for singularly perturbed equations. SIAM J., 19(1), 87-110.
21. Parsons, I., and Hall, J. (1990a). "The multigrid method in solid mechanics: Part I - algorithm description and behavior." Int. J. Numer. Methods in Engrg., 29, 719-737.
22. Parsons, I., and Hall, J. (1990b). "The multigrid method in solid mechanics: Part II - practical applications." Int. J. Numer. Methods in Engrg., 29, 739-753.
23. Rider, W., and Knoll, D. (1997). "Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods." Tech. Rep. LA-UR-97-2929, Los Alamos National Lab, Los Alamos, N.M.
24. Saad, Y. (1996). Iterative methods for sparse linear systems. PWS Publishing, Boston.
25. Zienkiewicz, O., and Taylor, R. (1994). The finite element method - volume I. McGraw-Hill, New York.
26. Zienkiewicz, O., Vilotte, J., Toyoshima, S., and Nakazawa, S. (1985). "Iterative methods for constrained and mixed approximation. An Inexpensive Improvement of FEM Performance." Computational Methods of Appl. Mech. and Engrg., 51, 3-29.