Algebraic multigrid methods for direct frequency response analyses in solid mechanics

Computational Mechanics

Volumn 39, Issue 4, 2007, Pages 497-507

  Adams, Mark F ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Algebraic multigrid; Direct frequency response analyses; Helmholtz equation solvers

Indexed keywords

COMPUTATIONAL METHODS; FREQUENCY RESPONSE; LINEAR EQUATIONS; LINEAR SYSTEMS; MATHEMATICAL OPERATORS;

ALGEBRAIC MULTIGRID; DIRECT FREQUENCY RESPONSE ANALYSES; HELMHOLTZ EQUATION SOLVERS;

LINEAR ALGEBRA;

EID: 33846250014     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0047-8     Document Type: Article

References (36)

1. Adams MF (1998) Multigrid equation solvers for large scale non-linear finite element simulations. Ph.D. dissertation, University of California. Berkeley, Technical report UCB//CSD-99-1033
2. Adams MF (1998) A parallel maximal independent set algorithm. In: Proceedings of the 5th copper mountain conference on iterative methods. Copper Mountain, CO
3. Adams MF (2000) Parallel multigrid solvers for 3D unstructured finite element problems in large deformation elasticity and plasticity. Int J Numer Methods Eng 48:1241-1262
4. Adams MF (2001) A distributed memory unstructured Gauss-Seidel algorithm for multigrid smoothers. In: ACM/IEEE proceedings of SC2001: high performance networking and computing. Denver, Colorado, November 2001
5. Adams MF (2002) Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics. Int J Numer Methods Eng 55:519-534
6. Adams MF, Brezina M, Hu JJ, Tuminaro RS (2003) Parallel multigrid smoothing: polynomial versus Gauss - Seidel. J Comp Phys 188:593-610
7. Balay S, Gropp WD, McInnes LC, Smith BF (1996) PETSc 2.0 users manual. Technical Report, Argonne National Laboratory
8. Bank RE (1981) A comparison of two multilevel iterative methods for nonsymmetric and indefinite elliptic finite element equations. SIAM J Numer Anal 18:724-743
9. Braess D (1986) On the combination of the multigrid method and conjugate gradients. In: Hackbusch W, Trottenberg U (eds) Multigrid methods II. Springer, Berlin Heidelberg Newyork, pp 52-64
10. Brandt A (1977) Multi-level adaptive solutions to boundary value problems. Math Comput 31:333-390
11. Brandt A, Livshits I (1997) Wave-ray multigrid method for standing wave equations. Electr Trans Num Anal 6:162-181
12. Briggs WL, Henson VE, McCormick S (2000) A multigrid tutorial, 2nd edn. SIAM, Philadelphia
13. Bulgakov VE, Kuhn G (1995) High-performance multilevel iterative aggregation solver for large finite-element structural analysis problems. Int J Numer Methods Eng 38:3529-3544
14. Chan TF, Smith BF (1994) Multigrid and domain decomposition on unstructured grids. In: Keyes D, Xu J (eds) 7th annual international conference on domain decomposition methods in scientific and engineering computing. AMS, 1995. A revised version of this paper appeared in ETNA, 2:171-182, December 1994
15. Craig RR (1981) Structural Dynamics: an introduction to computer methods. Wiley, NY
16. Day D, Heroux M (2001) Solving complex-valued linear systems via equivalent real formulations. SIAM J Sci Comput 23:480-498
17. Dendy J, Ida M, Rutledge J (1992) A semicoarsening multigrid algorithm for SIMD machines. SIAM J Sci Stat Comput 13:1460-1469
18. Elman H, Oliver G, O'Leary D (2001) A multigrid method enhanced by krylov subspace iteration for discrete helmholtz equations. SIAM J Sci Comput 23:1291-1315
19. Farhat C. Li J. An iterative domain decomposition method for the solution of a class of indefinite problems in computational structural dynamics. IMACS J Appl Numer Math (in press)
20. Farhat C, Roux F-X (1991) A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32:1205-1227
21. Fish J, Belsky V (1997) Generalized aggregation multilevel solver. Int J Numer Methods Eng 40:4341-4361
22. Guillard H (1993) Node-nested multi-grid with Delaunay coarsening. Technical Report 1898. Institute National de Recherche en Informatique et en Automatique
23. Hackbusch W (1985) Multi-grid methods and applications. Springer, Berlin Heidelberg Newyork
24. Hackbusch W (1985) Multigrid methods and applications. Computational mathematics, vol 4. Springer, Berlin Heidelberg Newyork
25. Karypis G, Kumar V (1996) Parallel multilevel k-way partitioning scheme for irregular graphs. In: ACM/IEEE Proceedings of SCI996: high performance networking and Computing
26. Lee B, Manteuffel T, McCormick S, Ruge J (2000) First-order systems least-squares (FOSLS) for the Helmholtz equation. SIAM J Sci Comput 21:1427-1449
27. Bhardwaj MM, Pierson K, Reese G, Walsh T, Day D, Alvin K, Peery J (2002) Salinas: a scalable software for high-performance structural and solid mechanics simulation. In: ACM/IEEE Proceedings of SC2002: high performance networking and computing. Gordon Bell Award
28. Mandel J, Brezina M, Vaněk P (1998) Energy optimization of algebraic multigridbases. Technical Report 125, UCD/CCM, February 1998
29. Mavriplis D (1999) Directional agglomeration multigrid techniques for high-Reynolds number viscous flows. AIAA J 37:1222-1230
30. Prometheus. http://www.cs.berkeley.edu/~madams
31. Saad Y (1993) A flexible inner-outer preconditioned gmres algorithm. SIAM J Sci Stat Comput 14:461-469
32. Saad Y, Schultz H (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856-869
33. Smith B, Bjorstad P, Gropp W (1996) Domain decomposition. Cambridge University Press, London
34. Trottenberg U, Oosterlee C, Schüller A (2001) Multigrid. Academic Press, London
35. Vaněk P, Mandel J (1995) Brezina M Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. In: Proceedings of the 7th copper mountain conference on multigrid methods, 1995
36. Yserentant H (1986) On the multilevel splitting of finite element spaces for indefinite elliptic boundary value problems. SIAM J Numer Anal 23:581-595