Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems

Computing (Vienna/New York)

Volumn 56, Issue 3, 1996, Pages 179-196

  Vanek P ^b   Mandel, J ^a   Brezina, M ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

Author keywords

Algebraic multigrid; Automatic coarsening; Biharmonic equation; Elasticity; Plates and shells; Unstructured meshes

Indexed keywords

ALGORITHMS; BENDING (DEFORMATION); COMPUTATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ELASTICITY; HEURISTIC METHODS; ITERATIVE METHODS; MATRIX ALGEBRA; PLATES (STRUCTURAL COMPONENTS); SHELLS (STRUCTURES);

ALGEBRAIC MULTIGRID; COARSE LEVELS; FOURTH ORDER ELLIPTIC PROBLEMS; NODAL COORDINATES; PLATE BENDING; SMOOTHED AGGREGATION; SOLID ELASTICITY; ZERO ENERGY MODES;

ALGEBRA;

EID: 0030388574     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02238511     Document Type: Article

References (21)

1. Alcouffe, R. E., Brandt, A., Dendy, J. E., Painter. J. W.: The multi-grid methods for the diffusion equation with strongly discontinuous coefficients. SIAM J. Sci. Stat. Comput. 2, 430-454 (1981)
2. 1 finite elements on nonnested meshes (submitted).
3. Bramble, J. H., Pasciak, J. E., Wang, J., Xu, J.: Convergence estimates for multigrip algorithms without regularity assumptions. Math. Comp. 57, 23-45 (1991).
4. Brandt, A.: Algebraic multigrid theory: The symmetric case. Appl. Math. Comput. 79, 23-56 (1986).
5. Brandt, A., McCormick, S. F., Ruge, J. W., Algebraic multigrid (AMG) for sparse matrix equations. In: Sparsity and its applications (Evans. D. J., ed.), pp. 257-284, Cambridge: Cambridge University Press 1985.
6. Brenner. S. C.: An optimal order nonconforming multigrid method for the biharmonic equation. SIAM J. Numer. Anal. 26, 1124-1138 (1989).
7. Chan, T. F., Go, S., Zou, J.: Multilevel domain decomposition and multigrid methods for unstructured meshes: algorithms and theory Tech. Report Cam 95-24. Dept. Math., UCLA, May 1995.
8. Dendy, J. E., Ida, M. P. Rutledge, J. M.: A semicoarsening multigrid algorithm for SIMD machines., SIAM J. Sci. Stat. Comput. 13, 1460-1469 (1992).
9. Hackbusch, W.: Multigrid methods and applications. Computational mathematics, Vol. 4. Berlin Heidelberg New York: Springer 1985.
10. Mandel, J.: Balancing domain decomposition. Comm. Numer. Meth. Eng. 9, 233-241 (1993).
11. Oswald, P.: Hierarchical conforming finite element methods for the biharmonic equation. SIAM J. Numer Anal. 29, 1620-1625 (1992).
12. Peisker, P., Braess, D.: A conjugate gradient method and a multigrid method for Morley's finite element approximation of the biharmonic equation. Numer. Math. 50, 567-586 (1987).
13. Ruge, J. W.: Algebraic multigrid (AMG) for geodetic survey problems, in Prelimary Proc. Internat. Multigrid Conference, Fort Collins, CO, 1983, Institute for Computational Studies at Colorado State University.
14. Ruge, J. W., Stuben, K.: Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG), In: Multigrid methods for integral and differential equations (Paddon, D. J., Holstein, H., eds.), pp. 169-212. The Institute of Mathematics and its Applications Conference Series, Oxford: Clarendon Press 1985.
15. Ruge, J. W., Stuben, K.: Algebraic multigrid (AMG) In: Multigrid methods (McCormick, S. F., ed.), pp. 73-130, Philadelphia: SIAM 1987.
16. Smith, R. A., Weiser, A.: Semicoarsening multigrid on a hypercube. SIAM J. Sci. Stat. Comput. 13, 1314-1329 (1992).
17. Stüben, K.: Algebraic multigrid (AMG): experiences and comparisons, Appl. Math. Comput. 13, 419-452 (1983).
18. Vanëk, P.: Fast multigrid solver. Appl. Math. 40, 1-20 (1995).
19. Vanëk, P.: Acceleration of convergence of a two-level algorithm by smoothing transfer operator. App. Math. 37, 265-274 (1992).
20. Vaněk, P., Mandel. J., Brezina, M.: Algebraic multigrid on unstructured meshes (Submitted).
21. Zhang, X.: Multilevel Schwarz methods for the biharmonic Dirichlet problem. SIAM J. Sci. Comput. 75, 621-644 (1994).