120
Views
22
CrossRef citations to date
0
Altmetric
Original Articles

Algebraic approach to absorbing boundary conditions for the Helmholtz equation

, &
Pages 231-240 | Received 19 Jan 2006, Published online: 21 May 2007

References

  • Antoine , X. , Bendali , A. and Darbas , M. 2005 . Analytic preconditionners for the boundary integral solution of the scattering of acoustic waves by open surfaces . Journal of Computational Acoustics , 13 : 477 – 498 .
  • Gander , M. J. and Nataf , F. 2005 . An incomplete LU preconditioner for problems in acoustics . Journal of Computational Acoustics , 13 : 455 – 476 .
  • Lee , B. , Manteuffel , T. , McCormick , S. and Ruge , J. Multilevel first-order system least squares for Helmholtz equation . 2nd Int. Conf. on Approx. and Num. Meths. for the Solution of the Maxwell Equations.
  • Vaněk , P. , Mandel , J. and Brezina , M. 1998 . Two-level algebraic multigrid for the Helmholtz problem . Contemporary Mathematics , 218 : 349 – 356 .
  • Gander , M. J. , Halpern , L. and Nataf , F. Optimized Schwarz methods . 12th Int. Conf. on Domain Decomposition Methods . pp. 15 – 28 .
  • 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 .
  • 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 .
  • Chevalier , P. and Nataf , F. 1998 . Symmetrized method with optimized second-order conditions for the Helmholtz equation . Contemporary Mathematics , 218 : 400 – 407 .
  • Després , B. Domain decomposition method and the Helmholtz problem. II . 2nd Int. Conf. on Math. and Numer. Aspects of Wave Propagation . pp. 197 – 206 . Philadelphia, PA : SIAM .
  • 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 .
  • 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 .
  • 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 .
  • Giorda , L. G. and Nataf , F. 2004 . “ Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients ” . CMAP, Ecole Polytechnique . Technical Report 561
  • 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 .
  • Farhat , C. and Roux , F.-X. 1994 . Implicit parallel processing in structural mechanics . Computational Mechanics Advances , 2 : 1 – 124 .
  • 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 .
  • Ghanemi , S. A domain decomposition method for Helmholtz scattering problems . 9th Int. Conf. on Domain Decomposition Methods . pp. 105 – 112 .
  • Nataf , F. , Rogier , F. and de Sturler , E. 1994 . “ Optimal interface conditions for domain decomposition methods ” . CMAP, Ecole Polytechnique . Technical Report
  • Saad , Y. 1996 . Iterative Methods for Linear Systems , Boston : PWS Publishing .
  • Karypis , G. and Kumar , V. 1995 . “ METIS: unstructured graph partitioning and sparse matrix ordering system – version 2.0 ” . University of Minnesota . Technical report, Departement of Computer Science
  • Karypis , G. and Kumar , V. 1997 . “ METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices ” . University of Minnesota . Technical report, Departement of Computer Science

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.