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

Mathematics and Computers in Simulation

Volumn 65, Issue 4-5, 2004, Pages 303-321

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

^a ÉCOLE DE TECHNOLOGIE SUPÉRIEURE   (Canada)

^b University of Minnesota   (United States)

Author keywords

Acoustic scattering; DtN technique; Finite element method; GMRES iterative method; Helmholtz equation; ILU0; ILUT; ILUTC; Incomplete factorization

Indexed keywords

ACOUSTIC WAVE SCATTERING; ALGORITHMS; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; GALERKIN METHODS; ITERATIVE METHODS; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING;

DTN TECQNIQUES; GMRES ITERATIVE METHOD; HELMHOLTZ EQUATION; ILUO; ILUT; ILUTC; INCOMPLETE FACTORIZATION;

ELECTROMAGNETIC WAVES;

EID: 2342510323     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2004.01.004     Document Type: Conference Paper

References (18)

1. Gunburger M., Bayliss A., Turkel E., Boundary conditions for the numerical solution of elliptic equations in exterior regions. SIAM J. Appl. Math. 42:1982;430-451.
2. Antoine X., Barucq H., Bendali A., Bayliss-Turkel like radiationcondition on surfaces of arbitrary shape. J. Math. Anal. Appl. 229:1999;184-211.
3. Berenger J.P., A perfectly matched layer for the absorption of electromagneticwaves. J. Comput. Phys. 114:1994;185-200.
4. J.J. Bowman, T.B. Senior, P.L.E. Uslenghi, Electromagnetic and acoustic scattering by simple shape. North-Holland, Amsterdam, 1969.
5. D. Colton, R. Kress. Inverse acoustic in electromagnetic scattering theory, in: Applied Mathematics Sciences, vol. 93, Springer, Berlin, 1992.
6. Djellouli R., Farhat C., Macedo A., Tezaur R., Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries. J. Comput. Acoust. 8(1):2000;81-99.
7. Enquist B., Majda A., Absorbing boundary conditions for the numericalsimulation of waves. Math. Comput. 31:1977;629-651.
8. Harari I., Grosh K., Hughes T.J.R., Malhotra M., Pinsky P.M., Stewart J.R., Thompson L.L., Recent developpments in finite element methods for structural acoustics. Archiv. Comput. Methods Eng. 3(2 y 3):1996;131-311.
9. Ihlenburg F., Babuska I., Finite element solution of the helmholtz equation with high wave number. i. the h-version of the fem. Comp. Math. Appl. 30:1995;9-37.
10. Keller J.B., Givoli D., Exact non reflecting boundary conditions. J. Comput. Phys. 82:1989;172-192.
11. N. Li, Y. Saad, E. Chow, Crout versions of ILU for general sparse matrices. Technical Report umsi-2002-021, Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN, 2002.
12. Mardochée Magolu Monga Madei, Incomplete factorization based preconditionings for solving the helmholtz equation. Int. J. Numer. Meth. Eng. 50 (2001) 1077-1101.
13. Oberai A.A., Pinsky P.M., A numerical comparaison of finite element methods for the helmholtz equation. J. Comput. Acoust. 8:2000;211-221.
14. Y. Saad, ILUT: a dual threshold incomplete ILU factorization. Numerical Linear Algebra Appl., 1 (1994) 387-402.
15. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Publishing, New York, 1996.
16. Saad Y., Schultz M.H., GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Scientific Stat. Comput. 7:1986;856-869.
17. Tezaur R., Macedo A., Farhat C., Djellouli R., Three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. Int. J. Numer. Meth. Eng. 53(1):2000;1461-1476.
18. A. Zebic, Equation de helmholtz: etude numérique de quelques preconditionneurs pour la méthode gmres. Technical Report 182, INRIA, 1992.