Preconditionning techniques for the solution of the Helmholtz equation by the finite element method

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2668, Issue , 2003, Pages 847-858

  Kechroud, Riyad ^a   Soulaimani, Azzeddine ^a   Saad, Yousef ^b  

^a ÉCOLE DE TECHNOLOGIE SUPÉRIEURE   (Canada)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GALERKIN METHODS; HELMHOLTZ EQUATION; ITERATIVE METHODS;

ACOUSTIC SCATTERING; DTN TECHNIQUE; ILU0; ILUT; INCOMPLETE FACTORIZATION;

FINITE ELEMENT METHOD;

EID: 35248889945     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44843-8_92     Document Type: Article

References (15)

1. M. Gunburger A. Bayliss and E. Turkel. Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM J. Appl. Math., 42:430-451, 1982.
2. X. Antoine, H. Barucq, and A. Bendali. Bayliss-turkel like radiationcondition on surfaces of arbitrary shape. J. Math. Anal. Appl., 229:184-211, 1999.
3. J.P. Berenger. A perfectly matched layer for the absorption of electromagneticwaves. J. Comput. Phys., 114:185-200, 1994.
4. R. Djellouli, C. Farhat, A. Macedo, and R. Tezaur. Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries. Journal of Computational Acoustics, 8(1):81-99, 2000.
5. B. Enquist and A. Majda. Absorbing boundary conditions for the numericalsimulation of waves. Math. Of Comput., 31:629-651, 1977.
6. I. Harrari, K. Grosch, T. J. R. Hughes, M. Malhotra, P.M. Pinsky, J. R. Stewart, and L. L. Thompson. Recent developpments in finite element methods for structural acoustics. Archives of Computional Methods in Engineering, 3, 2 y 3:131-311, 1996.
7. F. Ihlenburg and I. Babuska. Finite element solution of the helmholtz equation with high wave number, i. the h-version of the fem. Comp. Math. Appl., 30:9-37, 1995.
8. J.B. Keller and D. Givoli. Exact non reflecting boundary conditions. J.Comput. Phys., 82:172-192, 1989.
9. Mardochée Magolu Monga Madei. Incomplete factorization based preconditionings for solving the helmholtz equation. Int. J. Numer. Meth. Engng, 50:1077-1101, 2001.
10. A. A. Oberai and P. M. Pinsky. A numerical comparaison of finite element methods for the helmholtz equation. J. Comput. Acoustics, 8:211-221, 2000.
11. Y. Saad. ILUT: a dual threshold incomplete ILU factorization. Numerical Linear Algebra with Applications, 1:387-402, 1994.
12. Y. Saad. Iterative Methods for Sparse Linear Systems. PWS publishing, New York, 1996.
13. Y. Saad and M. H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7:856-869, 1986.
14. R. Tezaur, A. Macedo, C. Farhat, and R. Djellouli. Three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. Intern. J. for Numer. Meth. in Engin., 53(1):1461-1476, 2000.
15. A. Zebic. Equation de helmholtz: etude numérique de quelques preconditionneurs pour la méthode gmres. Technical Report 182, INRIA, 1992.