Free Access
Issue |
ESAIM: M2AN
Volume 50, Number 3, May-June 2016
Special Issue – Polyhedral discretization for PDE
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Page(s) | 921 - 944 | |
Section | Regular articles | |
DOI | https://doi.org/10.1051/m2an/2015058 | |
Published online | 23 May 2016 |
- I.M. Babuška, and S.A. Sauter, Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM Rev. 42 (2000) 451–484. [Google Scholar]
- A. Brandt and I. Livshits, Wave-ray multigrid method for standing wave equations, Electron. Trans. Numer. Anal. 6 (1997) 162–181. [MathSciNet] [Google Scholar]
- W. Chen, X. Xu and S. Zhang, On a Robin−Robin domain decomposition method with optimal convergence rate. J. Comput. Math. 32 (2014) 456–475. [Google Scholar]
- Q. Deng, A nonoverlapping domain decomposition method for nonconforming finite element problems. Commun. Pure Appl. Anal. 2 (2003) 295–306. [CrossRef] [Google Scholar]
- B. Despres, Domain Decomposition Method and Helmholtz Problem. Mathematical and Numerical Aspects of Wave Propagation Phenomena, edited by G. Cohen, L. Halpern and P. Joly. Philadelphia, SIAM (1991) 44–52. [Google Scholar]
- J. Douglas and C.S. Huang, An accelerated domain decomposition procedures based on Robin transmission conditions. BIT 37 (1997) 678-686. [CrossRef] [MathSciNet] [Google Scholar]
- J. Douglas and C.S. Huang, Accelerated domain decomposition iterative procedures for mixed methods based on Robin transmission conditions. Calcolo 35 (1998) 131–147. [CrossRef] [MathSciNet] [Google Scholar]
- O.G. Ernst and M.J. Gander, Why is Difficult to Solve Helmholtz Problems with Classical Iterative Methods. Numerical Analysis of Multiscale Problems, edited by I. Graham, T. Hou, O. Lakkis and R. Scheichl. Springer-Verlag, New York (2011) 325–363. [Google Scholar]
- C. Farhat, A. Macedo and R. Tezaur, FETI-H: A Scalable Domain Decomposition Method for High Frequency Exterior Helmholtz Problem. In 11th International Conference on Domain Decomposition Method, edited by P. Bjørstad, M. Cross and O. Widlund. Choi-Hong Lai, DDM.ORG (1999) 231–241. [Google Scholar]
- C. Farhat, P. Avery, R. Tezaur and J. Li, FETI-DPH: a dual-primal domain decomposition method for accoustic scattering. J. Comput. Acoustics 13 (2005) 499–524. [CrossRef] [Google Scholar]
- M.J. Gander, L. Halpern and F. Nataf, Optimized Schwarz Methods. In 12th International Conference on Domain Decomposition Methods, edited by T. Chan, T. Kako, H. Kawarada and O. Pironneau. Chiba, Japan, Domain Decomposition Press (2001) 15–18. [Google Scholar]
- M.J. Gander, L. Halpern and F. Magoules, An optimized Schwarz method with two-sided Robin transmission conditions for the Helmholtz equation. Int. J. Numer. Meth. Fluids 55 (2007) 163–175. [CrossRef] [MathSciNet] [Google Scholar]
- M.J. Gander, F. Magoules and F. Nataf, Optimized Schwarz methods without overlap for the Helmholtz equation. SIAM J. Sci. Comput. 24 (2002) 38–60. [Google Scholar]
- W. Guo and L.S. Hou, Generalization and accelerations of Lions’ nonoverlapping domain decomposition method for linear elliptic PDE. SIAM J. Numer. Anal. 41 (2003) 2056–2080. [Google Scholar]
- F. Ihlenburg, Finite Element Analysis of Acoustic Scattering. Vol. 132 of Appl. Math. Sci. Springer-Verlag, New York (1998). [Google Scholar]
- J. Li and X. Tu, Convergence analysis of a balancing domain decomposition method for solving a class of indefinite linear systems. Numer. Linear Algebra Appl. 16 (2009) 745–773. [Google Scholar]
- L. Qin and X. Xu, On a parallel Robin-type nonoverlapping domain decomposition method. SIAM J. Numer. Anal. 44 (2006) 2539–2558. [Google Scholar]
- L. Qin, Z. Shi and X. Xu, On the convergence rate of a parallel nonoverlapping domain decomposition method. Sci. China, Ser. A: Math. 51 (2008) 1461–1478. [CrossRef] [Google Scholar]
- A. Toselli and O. Widlund, Domain Decomposition Methods-Algorithms and Theory. Vol. 34 of Springer Ser. Comput. Math. Springer-Verlag, Berlin (2005). [Google Scholar]
- M.B. Van Gijzen, Y.A. Erlangga and C. Vuik, Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian. SIAM J. Sci. Comput. 29 (2007) 1942–1958. [Google Scholar]
- X. Xu and L. Qin, Spectral analysis of DN operators and optimized Schwarz methods with Robin transmission conditions. SIAM J. Numer. Anal. 47 (2010) 4540–4568. [Google Scholar]
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