Parallel algebraic multigrids for structural mechanics

SIAM Journal on Scientific Computing

Volumn 27, Issue 5, 2006, Pages 1534-1554

  Brezina, Marian ^a,b   Tong, Charles ^c   Becker, Richard ^c  

^a UNIVERSITY OF COLORADO   (United States)

^b Front Range Scientific Computations Inc ^*  (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Algebraic multigrid; Parallel computing; Preconditioning

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; NUMERICAL ANALYSIS; PARALLEL PROCESSING SYSTEMS; PROBLEM SOLVING;

ALGEBRAIC MULTIGRIDS (AMG); MULTIGRID METHODS; PRECONDITIONING;

DATA STRUCTURES;

EID: 33748801751     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040608271     Document Type: Conference Paper

References (29)

1. M. F. ADAMS, A distributed memory unstructured Gauss-Seidel algorithm, for multigrid smoothers, in ACM/IEEE Proceedings of SC2001: High Performance Networking and Computing, Denver, CO, 2001.
2. M. F. ADAMS, M. BREZINA, J. J. HU, AND R. S. TUMINARO, Parallel multigrid smoothing: Polynomial versus GS, J. Comput. Phys., 188 (2003), pp. 593-610.
3. ALE3D Theory Manual, UCRL-PRES-203313, Lawrence Livermore National Laboratory, Livermore, CA.
4. P. B. BOCHEV, C. J. GARASI, J. J. HU, A. C. ROBINSON, AND R. S. TUMINARO, An improved algebraic multigrid method for solving Maxwell's equations, SIAM J. Sci. Comput., 25 (2003), pp. 623-642.
5. A. BRANDT, S. F. MCCORMICK, AND J. W. RUGE, Algebraic Multigrid (AMG) for Automatic Multigrid Solutions with Application to Geodetic Computations, Technical Report, Inst. for Computational Studies, Fort Collins, CO, 1982.
6. M. BREZINA, A. J. CLEARY, R. D. FALGOUT, V. E. HENSON, J. E. JONES, T. A. MANTEUFFEL, S. F. MCCORMICK, AND J. W. RUGE, Algebraic multigrid based on element interpolation (AMGe), SIAM J. Sci. Comput., 22 (2000), pp. 1570-1592.
7. M. BREZINA, C. HEBERTON, AND P. VANĚK, An Iterative Method with Convergence Rate Chosen A Priori, UCD/CCM Report 140, Center for Computational Mathematics, University of Colorado at Denver, Denver, CO, 1999.
8. M. BREZINA, R. FALGOUT, S. MACLACHLAN, T. MANTEUFFEL, S. MCCORMICK, AND J. RUGE, Adaptive smoothed aggregation (αSA), SIAM J. Sci. Comput., 25 (2004), pp. 1896-1920.
9. M. BREZINA AND P. VANĚK, A Black-box Iterative solver based on a two-level Schwarz method, Computing, 63 (1999), pp. 233-263.
10. T. CHARTIER, R. D. FALGOUT, V. E. HENSON, J. JONES, T. MANTEUFFEL, S. MCCORMICK, J. RUGE, AND P. S. VASSILEVSKI, Spectral AMGe (pAMGe), SIAM J. Sci. Comput., 25 (2003), pp. 1-26.
11. A. J. CLEARY, R. D. FALGOUT, V. E. HENSON, AND J. E. JONES, Coarse grid selection for parallel algebraic multigrid, in Proceedings of the Fifth International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Comput. Sci. 1457, Springer-Verlag, New York, 1998, pp. 104-115.
12. M. CONSIDÈRE, Die Anwendung von Eisen und Stahl bei Konstruktionen, Gerold-Verlag, Wien, 1888.
13. J. FISH AND V. BELSKY, Generalized Aggregation Multilevel Solver, Internat. J. Numer. Methods Engrng., 40 (1997), pp. 4341-4361.
14. R. D. FALGOUT AND U. M. YANG, hypre: A library of high performance preconditioned, in Computational Science (CARS 2002, Part III), Lecture Notes in Comput. Sci. 2331, Springer-Verlag, New York, 2002, pp. 632-641.
15. G. HAASE, M. KUHN, AND S. REITZINGER, Parallel algebraic multigrid methods on distributed memory computers, SIAM J. Sci. Comput., 24 (2002), pp. 410-427.
16. V. E. HENSON AND U. M. YANG, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math., 41 (2002), pp. 155-177.
17. M. T. JONES AND P. E. PLASSMANN, A parallel graph coloring heuristic, SIAM J. Sci. Comput. 14 (1993), pp. 654-669.
18. A. KRECHEL AND K. STÜBEN, Parallel algebraic multigrid based on subdomain blocking, Parallel Computing, 27 (2001), pp. 1009-1031.
19. M. LUBY, A simple parallel algorithm for maximal independent set problem, SIAM J. Comput., 15 (1986), pp. 1036-1053.
20. J. MANDEL, Adaptive iterative solvers in finite elements, in Solving Large-Scale Problems in Mechanics, M. Papadrakakis, ed., John Wiley & Sons, Chichester, UK, 1993, pp. 65-86.
21. J. MANDEL, Iterative methods for p-version finite elements: Preconditioning thin solids, Comput. Methods Appl. Mech. Engrg., 133 (1996), pp. 247-257.
22. J. W. RUGE AND K. STÜBEN, Algebraic multigrid, in Multigrid Methods, S. F. McCormick, ed., Frontiers Appl. Math., SIAM, Philadelphia, 1987, pp. 73-130.
23. Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869.
24. C. H. TONG AND R. S. TUMINARO, Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines, in Proceedings of Supercomputing, 2000.
25. P. VANĚK, Acceleration of convergence of a two-level algorithm by smooth transfer operators, Appl. Math., 37 (1992), pp. 265-274.
26. P. VANĚK, M. BREZINA, AND J. MANDEL, Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math., 88 (2001), pp. 559-579.
27. P. VANĚK, M. BREZINA, AND R. TEZAUR, Two-grid method for linear elasticity on unstructured meshes, SIAM J. Sci. Comput., 21 (1999), pp. 900-923.
28. P. VANĚK, J. MANDEL, AND M. BREZINA, Algebraic multigrid based on smoothed aggregation for second and fourth order problems, Computing, 56 (1996), pp. 179-196.
29. U. M. YANG, On the use of relaxation parameters in hybrid smoothers, Numer. Linear Algebra Appl., 11 (2004), pp. 155-172.