Parallel multigrid solver for 3D unstructured finite element problems

ACM/IEEE SC 1999 Conference, SC 1999

Volumn , Issue , 1999, Pages 27-

  Adams, Mark ^a   Demmel, James W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Parallel maximal independent sets; Parallel sparse solvers; Unstructured multigrid

Indexed keywords

ALGEBRA; DEGREES OF FREEDOM (MECHANICS); LINEAR ALGEBRA; LINEAR EQUATIONS;

DEFORMATION ELASTICITY; FINITE ELEMENT PROBLEMS; INHERENT FLEXIBILITY; MAXIMAL INDEPENDENT SET; MULTI-GRID; MULTI-GRID ALGORITHMS; PARALLEL SPARSE SOLVERS; SYSTEM OF LINEAR ALGEBRAIC EQUATIONS;

FINITE ELEMENT METHOD;

EID: 85015330781     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SC.1999.10033     Document Type: Conference Paper

References (26)

1. M. F. Adams. Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations. Ph.D. dissertation, University of California, Berkeley, 1998. Tech. report UCB//CSD-99-1033.
2. M. F. Adams. A parallel maximal independent set algorithm. In Proceedings 5th copper mountain conference on iterative methods, 1998. Best student paper award winner.
3. S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.
4. W. Briggs. A Multigrid Tutorial. SIAM, 1987.
5. V.E. Bulgakov and G. Kuhn. High-performance multilevel iterative aggregation solver for large finite-element structural analysis problems. International Journal for Numerical Methods in Engineering, 38, 1995.
6. T. F. Chan and B. F. Smith. Multigrid and domain decomposition on unstructured grids. In David F. Keyes and Jinchao Xu, editors, Seventh Annual International Conference on Domain Decomposition Methods in Scientific and Engineering Computing. AMS, 1995. A revised version of this paper has appeared in ETNA, 2:171-182, December 1994.
7. J. Demmel. Applied Numerical Linear Algebra. SIAM, 1997.
8. M.C. Dracopoulos and M.A Crisfield. Coarse/fine mesh preconditioners for the iterative solution of finite element problems. International Journal for Numerical Methods in Engineering, 38:3297-3313, 1995.
9. FEAP. http://www.ce.berkeley.edu/~ rlt.
10. D. A. Field. Implementing Watson's algorithm in three dimensions. In Proc. Second Ann. ACM Symp. Comp. Geom., 1986.
11. J. Fish, V. Belsky, and S. Gomma. Unstructured multigrid method for shells. International Journal for Numerical Methods in Engineering, 39:1181-1197, 1996.
12. J. Fish, M. Pandheeradi, and V. Belsky. An efficient multilevel solution scheme for large scale non-linear systems. International Journal for Numerical Methods in Engineering, 38:1597-1610, 1995.
13. H. Guillard. Node-nested multi-grid with Delaunay coarsening. Technical Report 1898, Institute National de Recherche en Informatique et en Automatique, 1993.
14. M. T. Jones and P. E. Plassman. A parallel graph coloring heuristic. SIAM J. Sci. Comput., 14(3):654-669, 1993.
15. S. Kacau and I. D. Parsons. A parallel multigrid method for history-dependent elastoplacticity computations. Computer methods in applied mechanics and engineering, 108, 1993.
16. George Karypis and Kumar Vipin. Parallel multilevel k-way partitioning scheme for irregular graphs. Supercomputing, 1996.
17. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 4:1036-1053, 1986.
18. D.R.J. Owen, Y.T. Feng, and D Peric. A multi-grid enhanced GMRES algorithm for elasto-plastic problems. International Journal for Numerical Methods in Engineering, 42:1441-1462, 1998.
19. Prometheus. http://www.cs.berkeley.edu/~madams/Prometheus-1.1.
20. J. Ruge. AMG for problems of elasticity. Applied Mathematics and Computation, 23:293-309, 1986.
21. J. R. Shewchuk. Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. Discrete & Computational Geometry, 18(3):305-363, October 1997.
22. J.C. Simo and T.J.R. Hughes. Computational Inelasticity. Springer-Verlag, 1998.
23. B. Smith, P. Bjorstad, and W. Gropp. Domain Decomposition. Cambridge University Press, 1996.
24. S. Toledo. Improving memory-system performance of sparse matrix-vector multiplication. In Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing, March 1997.
25. P. Vanek, J. Mandel, and M. Brezina. Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. In 7th Copper Mountain Conference on Multigrid Methods, 1995.
26. O.C. Zienkiewicz and R.L. Taylor. The Finite Element Method, volume 1. McGraw-Hill, London, Fourth edition, 1989.