AILU for Helmholtz problems: A new preconditioner based on the analytic parabolic factorization

Journal of Computational Acoustics

Volumn 9, Issue 4, 2001, Pages 1499-1506

  Gander, Martin J ^a   Nataf, Frédéric ^b  

^a MCGILL UNIVERSITY   (Canada)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035567809     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X01001510     Document Type: Article

References (13)

1. M. Benzi and M. Tuma, "A comparative study of sparse approximate inverse preconditioned," Technical Report LA-UR-98-0024, Los Alamos National Laboratory, 1998.
2. X.-C. Cai, M. A. Casarin, F. W. Jr. Elliott, and O. B. Widlund, "Overlapping Schwarz algorithms for solving Helmholtz's equation," in Domain decomposition methods, 10 Boulder, CO, 1997, (Amer. Math. Soc., Providence, RI, 1998), pp. 391-399.
3. P. Chevalier and F. Nataf, "Symmetrized method with optimized second-order conditions for the Helmholtz equation," in Domain Decomposition Methods, 10 Boulder, CO, 1997 (Amer. Math. Soc., Providence, RI, 1998), pp. 400-407.
4. J. F. Claerbout, Fundamentals of Geophysical Data Processing with Applications to Petroleum Prospecting (McGraw-Hill, 1976).
5. A. de La Bourdonnaye, C. Farhat, A. Macedo, F. Magoulès, and F.-X. Roux, "A non-overlapping domain decomposition method for exterior Helmholtz problem," in Domain Decomposition Methods, 10 Boulder, CO, 1997 (Amer. Math. Soc., Providence, RI, 1998), pp. 42-66.
6. B. Després, "Domain decomposition method and the Helmholtz problem," in Mathematical and Numerical Aspects of Wave Propagation Phenomena (SIAM, Philadelphia, PA, 1991), pp. 44-52.
7. E. Giladi and J. B. Keller, "Iterative solution of elliptic problems by approximate factorization," J. Computational and Applied Mathematics, 85, 287 (1997).
8. F. Nataf, "Résolution de l'équation de convection-diffusion stationaire par une factorisation parabolique," C. R. Acad. Sci., Paris 1310(13), 869 (1990).
9. F. Nataf, J. P. Loheac, and M. Schatzman, "Parabolic approximation of the convection-diffusion equation," Math. Comp. 60, 515 (1993).
10. J. Stoer and R. Bulirsch, Numerical Analysis (Springer, Berlin, 1993).
11. C. Wagner, "Tangential frequency filtering decompositions for symmetric matrices," Numer. Math. 78(1), 119 (1997).
12. G. Wittum, "An ILU-based smoothing correction scheme," in Parallel Algorithms for Partial Differential Equations - Proc. 6th GAMM-Semin., Kiel/Ger., Notes Numer. Fluid Mech. 31, 228 (1991).
13. G. Wittum, Filternde Zerlegungen. Schnelle Löser fuer grosse Gleichungssysteme (Teubner Skripten zur Numerik, Stuttgart, 1992).