Algebraic approach to absorbing boundary conditions for the Helmholtz equation

International Journal of Computer Mathematics

Volumn 84, Issue 2, 2007, Pages 231-240

  Magoules F ^a   Roux, F X ^b   Series, L ^b  

^a Ecole Centrale de Paris   (France)

^b ONERA   (France)

Author keywords

Absorbing boundary condition; Acoustics; Algebraic patch substructuring; Coarse grid; Domain decomposition

Indexed keywords

ACOUSTICS; ALGEBRA; BOUNDARY CONDITIONS; COMPUTATION THEORY; FOURIER TRANSFORMS; NUMERICAL METHODS; PROBLEM SOLVING;

ABSORBING BOUNDARY CONDITION; ALGEBRAIC PATCH SUBSTRUCTURING; COARSE GRID; DOMAIN DECOMPOSITION;

HELMHOLTZ EQUATION;

EID: 34249033416     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160601168605     Document Type: Conference Paper

References (21)

1. Antoine, X., Bendali, A. and Darbas, M., 2005, Analytic preconditionnera for the boundary integral solution of the scattering of acoustic waves by open surfaces. Journal of Computational Acoustics, 13, 477-498.
2. Gander, M.J. and Nataf, F., 2005, An incomplete LU preconditioner for problems in acoustics. Journal of Computational Acoustics, 13, 455-476.
3. Lee, B., Manteuffel, T., McCormick, S. and Ruge, J., 1993, Multilevel first-order system least squares for Helmholtz equation. In 2nd Int. Conf. on Approx. and Num. Meths. for the Solution of the Maxwell Equations.
4. Vaněk, P., Mandel, J. and Brezina, M., 1998, Two-level algebraic multigrid for the Helmholtz problem. Contemporary Mathematics, 218, 349-356.
5. Gander, M.J., Halpern, L. and Nataf, F., 2001, Optimized Schwarz methods. In 12th Int. Conf. on Domain Decomposition Methods, pp. 15-28.
6. Farhat, C., Avery, P., Tezaur, R. and Li, J., 2005, FETI-DPH: A dual-primal domain decomposition method for acoustic scattering. Journal of Computational Acoustics, 13, 499-524.
7. Benamou, J.-D. and Després, B., 1997, A domain decomposition method for the Helmholtz equation and related optimal control problems. Journal of Computational Physics, 136, 68-82.
8. Chevalier, P. and Nataf, F., 1998, Symmetrized method with optimized second-order conditions for the Helmholtz equation. Contemporary Mathematics, 218, 400-407.
9. Després, B., 1993, Domain decomposition method and the Helmholtz problem. II. In 2nd Int. Conf. on Math. and Numer. Aspects of Wave Propagation (Philadelphia, PA: SIAM), pp. 197-206.
10. Gander, M.J., Magoulès, F. and Nataf, F., 2002, Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM Journal of Scientific Computing, 24, 38-60.
11. Magoulès, F., Ivànyi, P. and Topping, B.H.V., 2004, Non-overlapping Schwarz methods with optimized transmission conditions for the Helmholtz equation. Computer Methods in Applied Mechanics and Engineering, 193, 4797-4818.
12. Magoulès, F., Roux, F.-X. and Salmon, S., 2004, Optimal discrete transmission conditions for a non-overlapping domain decomposition method for the Helmholtz equation. SIAM Journal of Scientific Computing, 25, 1497-1515.
13. Giorda, L.G. and Nataf, F., 2004, Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients. Technical Report 561, CMAP, Ecole Polytechnique.
14. Magoulès, F., Roux, F.-X. and Series, L., 2005, Algebraic way to derive absorbing boundary conditions for the Helmholtz equation. Journal of Computational Acoustics, 13, 433-454.
15. Farhat, C. and Roux, F.-X., 1994, Implicit parallel processing in structural mechanics. Computational Mechanics Advances, 2, 1-124.
16. Farhat, C., Macedo, A., Lesoinne, M., Roux, F.-X., Magoulès F. and de la Bourdonnaye, A., 2000, Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Computer Methods in Applied Mechanics and Engineering, 184, 213-240.
17. Ghanemi, S., 1997, A domain decomposition method for Helmholtz scattering problems. In 9th Int. Conf. on Domain Decomposition Methods, pp. 105-112.
18. Nataf, F., Rogier, F. and de Sturler, E., 1994, Optimal interface conditions for domain decomposition methods. Technical Report, CMAP, Ecole Polytechnique.
19. Saad, Y., 1996, Iterative Methods for Linear Systems (Boston: PWS Publishing).
20. Karypis, G. and Kumar, V., 1995, METIS: unstructured graph partitioning and sparse matrix ordering system version 2.0. Technical report, Departement of Computer Science, University of Minnesota.
21. Karypis, G. and Kumar, V., 1997, METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. Technical report, Departement of Computer Science, University of Minnesota.