Incremental spectral preconditioners for sequences of linear systems

Applied Numerical Mathematics

Volumn 57, Issue 11-12, 2007, Pages 1164-1180

  Giraud, L ^a   Gratton, S ^a   Martin, E ^a  

^a CERFACS   (France)

Author keywords

Implicitly restarted Arnoldi method; Krylov solvers; Large parallel calculations; Spectral preconditioners

Indexed keywords

COMPUTATION THEORY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; MATLAB;

ELECTROMAGNETIC SIMULATIONS; IMPLICITLY RESTARTED ARNOLDI METHOD; KRYLOV SOLVERS; LARGE PARALLEL CALCULATIONS; SPECTRAL PRECONDITIONERS;

LINEAR SYSTEMS;

EID: 34548310326     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2007.01.005     Document Type: Article

References (30)

1. Alléon G., Benzi M., and Giraud L. Sparse approximate inverse preconditioning for dense linear systems arising in computational electromagnetics. Numerical Algorithms 16 (1997) 1-15
2. Baglama J., Calvetti D., Golub G.H., and Reichel L. Adaptively preconditioned GMRES algorithms. SIAM J. Scientific Computing 20 1 (1999) 243-269
3. Benzi M., and Tůma M. A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM J. Scientific Computing 19 3 (1998) 968-994
4. Carpentieri B., Duff I.S., and Giraud L. A class of spectral two-level preconditioners. SIAM J. Scientific Computing 25 2 (2003) 749-765
5. Carpentieri B., Duff I.S., Giraud L., and Sylvand G. Combining fast multipole techniques and an approximate inverse preconditioner for large parallel electromagnetics calculations. SIAM J. Scientific Computing 27 3 (2005) 774-792
6. Colton D., and Kress R. Integral Equation Methods in Scattering (1983), Wiley & Sons, New York
7. Darve E. The fast multipole method (I): Error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38 1 (2000) 98-128
8. Darve E. The fast multipole method: Numerical implementation. J. Comp. Phys. 160 1 (2000) 195-240
9. E. de Sturler, Inner-outer methods with deflation for linear systems with multiple right-hand sides, in: Householder Symposium XIII, Proceedings of the Householder Symposium on Numerical Algebra, Pontresina, Switzerland, June 17-26, 1996, pp. 193-196
10. Duff I.S., Giraud L., Langou J., and Martin E. Using spectral low rank preconditioners for large electromagnetic calculations. Int. J. Numer. Methods Engrg. 62 3 (2005) 416-434
11. Erhel J., Burrage K., and Pohl B. Restarted GMRES preconditioned by deflation. J. Comput. Appl. Math. 69 (1996) 303-318
12. Frank J., and Vuik C. A comparison of deflation and coarse grid correction applied to porous media flow. SIAM J. Numer. Anal. 42 4 (2004) 1631-1647
13. Freund R.W., and Malhotra M. A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides. Linear Algebra Appl. 254 (1997) 119-157
14. L. Giraud, S. Gratton, On the sensitivity of some spectral preconditioners, Technical Report TR/PA/04/1008, CERFACS, Toulouse, France, 2004
15. Giraud L., Langou J., and Sylvand G. On the parallel solution of large industrial wave propagation problems. Journal of Computational Acoustics 14 1 (2006) 83-111
16. Golub G.H., and Van Loan C.F. Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. third ed. (1996), The Johns Hopkins University Press, Baltimore, MD
17. Grote M., and Huckle T. Parallel preconditionings with sparse approximate inverses. SIAM J. Sci. Comput. 18 3 (1997) 838-853
18. Morgan R.B. A restarted GMRES method augmented with eigenvectors. SIAM J. Matrix Anal. Appl. 16 4 (1995) 1154-1171
19. Morgan R.B. Harmonic projection methods for large non-symmetric eigenvalue problems. Numer. Linear Algebra Appl. 5 (1998) 33-55
20. Morgan R.B. Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations. SIAM J. Matrix Anal. Appl. 21 4 (2000) 1112-1135
21. Morgan R.B. GMRES with deflated restarting. SIAM J. Sci. Comput. 24 1 (2002) 20-37
22. O'Leary D.P. The block conjugate gradient algorithm and related methods. Linear Algebra Appl. 29 (1980) 293-322
23. M.L. Parks, E. de Sturler, G. Mackey, D.D. Jhonson, S. Maiti, Recycling Krylov subspaces for sequences of linear systems, Technical Report UIUCDCS-R-2004-2421 (CS), University of Illinois at Urbana-Champaign, 2004
24. J.-C. Rioual, Solving linear systems for semiconductor device simulations on parallel distributed computers, PhD thesis, CERFACS, Toulouse, France, 2002
25. Saad Y. ILUT: A dual threshold incomplete LU factorization. Numer. Linear Algebra Appl. 1 (1994) 387-402
26. Saad Y., and Schultz M.H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 3 (1986) 856-869
27. Simoncini V., and Gallopoulos E. An iterative method for nonsymmetric systems with multiple right-hand sides. SIAM J. Sci. Comput. 16 4 (1995) 917-933
28. G. Sylvand, La méthode multipôle rapide en électromagnétisme : performances, parallélisation, applications, PhD thesis, Ecole Nationale des Ponts et Chaussées, 2002
29. B. Vital, Étude de quelques méthodes de résolution de problèmes linéaires de grande taille sur multiprocesseur, PhD dissertation, Université de Rennes, November 1990
30. Waisman H., Fish J., Tuminaro R.S., and Shadid J. The generalized global basis method. Int. J. Numer. Methods Engrg. 61 (2004) 1243-1269