Multigrid methods for 3-D definite and indefinite problems

Applied Numerical Mathematics

Volumn 26, Issue 3, 1998, Pages 377-398

  Shapira, Yair ^a,b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE VOLUME METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING;

HELMHOLTZ EQUATIONS; MULTIGRID METHODS; MULTILEVEL ANALYSIS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032019318     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00070-6     Document Type: Article

References (26)

1. R. Alcouffe, A. Brandt, J.E. Dendy and J. Painter, The multigrid method for the diffusion equation with strongly discontinuous coefficients, SIAM J. Sci. Statist. Comput. 2 (1981) 430-454.
2. K. Brackenridge, Multigrid and cyclic reduction applied to the Helmholtz equation, in: N.D. Melson, S.F. McCormick and T.A. Manteuffel, eds., Sixth Copper Mountain Conference on Multigrid Methods (NASA, Langley Research Center, Hampton, VA, 1993) 31-42.
3. J.H. Bramble, Z. Leyk and J.E. Pasciak, Iterative schemes for non-symmetric and indefinite elliptic boundary value problems, Math. Comp. 60 (1993) 1-22.
4. A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31 (1977) 333-390.
5. A. Brandt, Guide to multigrid development, in: W. Hackbusch and U. Trottenberg, eds., Multigrid Methods, Lecture Notes in Mathematics 960 (Springer, Berlin, 1982).
6. A. Brandt and S. Ta'asan, Multigrid methods for nearly singular and slightly indefinite problems, in: W. Hackbusch and U. Trottenberg, eds., Multigrid Methods II, Proceedings, Cologne, 1985, Lecture Notes in Mathematics 1228 (Springer, Berlin, 1985) 100-122.
7. A. Brandt and I. Yavneh, Accelerated multigrid convergence and high Reynolds recirculating flows, SIAM J. Sci. Statist. Comput. 14 (1993) 607-626.
8. J.E. Dendy, Black box multigrid, J. Comput. Phys. 48 (1982) 366-386.
9. J.E. Dendy, Two multigrid methods for the three-dimensional problems with discontinuous and anisotropic coefficients, SIAM J. Sci. Statist. Comput. 8 (1987) 673-685.
10. P.M. de Zeeuw, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J. Comput. Appl. Math. 33 (1990) 1-27.
11. P.O. Frederickson and O.A. McBryan, Parallel superconvergent multigrid, in: S.F. McCormick, ed., Multigrid Methods, Lecture Notes in Pure and Applied Mathematics 110 (Marcel Dekker, New York, 1988).
12. R.W. Freund, Conjugate gradients type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Statist. Comput. 13 (1992) 425-448.
13. R.W. Freund, Transpose free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Statist. Comput. 14 (1993) 470-482.
14. W. Hackbusch, Multigrid Methods and Applications (Springer, Berlin, 1985).
15. R. Kettler, Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradients methods, in: W. Hackbusch and U. Trottenberg, eds., Multigrid Methods, Lecture Notes in Mathematics 960 (Springer, Berlin, 1982).
16. Y. Saad and M.H. Schultz, A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 7 (1986) 856-869.
17. Y. Shapira, Analysis of matrix-dependent multigrid algorithms, Numer. Linear Algebra Appl., submitted.
18. Y. Shapira, Coloring update methods, BIT 38 (1) (1998) 169-177.
19. Y. Shapira, Multigrid techniques for highly indefinite equations, in: N.D. Melson, T.A. Manteuffel, S.F. McCormick and C.C. Douglas, eds., Seventh Copper Mountain Conference on Multigrid Methods (NASA, Hampton, VA, 1996) 689-705.
20. Y. Shapira, M. Israeli and A. Sidi, An automatic multigrid method for the solution of sparse linear systems, in: N.D. Melson, S.F. McCormick and T.A. Manteuffel, eds., Sixth Copper Mountain Conference on Multigrid Methods (NASA, Langley Research Center, Hampton, VA, 1993) 567-582.
21. Y. Shapira, M. Israeli and A. Sidi, Towards automatic multigrid algorithms for SPD, nonsymmetric and indefinite problems, SIAM J. Sci. Comput. 17 (1996) 439-453.
22. Y. Shapira, A. Sidi and M. Israeli, A parallelizable incomplete LU-type preconditioner for the solution of sparse linear systems, Technical Report #799, Computer Science Department, Technion - Israel Institute of Technology (1993).
23. P. Sonneveld, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 10 (1989) 36-52.
24. P. Sonneveld, P. Wesseling and P.M. de Zeeuw, Multigrid and conjugate gradient methods as convergence acceleration techniques, in: D.J. Paddon and H. Holstein, eds., Multigrid Methods for Integral and Differential Equations (Oxford University Press, Oxford, 1985) 117-168.
25. R. Varga, Matrix Iterative Analysis (Prentice-Hall. Englewood Cliffs, NJ, 1962).
26. D. Young, Iterative Solution of Large Linear Systems (Academic Press, New York, 1971).