Free Access
Issue |
ESAIM: M2AN
Volume 46, Number 3, May-June 2012
Special volume in honor of Professor David Gottlieb
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Page(s) | 647 - 660 | |
DOI | https://doi.org/10.1051/m2an/2011063 | |
Published online | 11 January 2012 |
- 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. Bayliss, C.I. Goldstein and E. Turkel, An iterative method for the Helmholtz equation. J. Comput. Phys. 49 (1983) 443–457. [CrossRef] [Google Scholar]
- A. Bayliss, C.I. Goldstein and E. Turkel, On accuracy conditions for the numerical computation of waves. J. Comput. Phys. 59 (1985) 396–404. [CrossRef] [Google Scholar]
- A. Brandt, Multi-level adaptive solution to the boundary- value problems. Math. Comp. 31 (1977) 333-390. [Google Scholar]
- A. Brandt and I. Livshits, Remarks on the wave-ray Multigrid Solvers for Helmholtz Equations, Computational Fluid and Solid Mechanics, edited by K.J. Bathe. Elsevier (2003) 1871–1871. [Google Scholar]
- H.C. Elman and D.P. O’Leary, Efficient iterative solution of the three dimensional Helmholtz equation. J. Comput. Phys. 142 (1998) 163–181. [CrossRef] [Google Scholar]
- Y.A. Erlangga, Advances in iterative methods and preconditioners for the Helmholtz equation. Arch. Comput. Methods Eng. 15 (2008) 37–66. [CrossRef] [MathSciNet] [Google Scholar]
- Y.A. Erlangga, C. Vuik and C.W. Oosterlee, On a class of preconditioners for the Helmholtz equation. Appl. Numer. Math. 50 (2004) 409–425. [CrossRef] [Google Scholar]
- Y.A. Erlangga, C.W. Oosterlee and C. Vuik, A novel multigrid based preconditioner for heterogeneous Helmholtz problems. SIAM J. Sci. Comput. 27 (2006) 1471–1492. [CrossRef] [Google Scholar]
- Y.A. Erlangga, C. Vuik and C.W. Oosterlee, Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation. Appl. Numer. Math. 56 (2006) 648–666. [CrossRef] [Google Scholar]
- G.R. Hadley, A complex Jacobi iterative method for the indefinite Helmholtz equation. J. Comput. Phys. 203 (2005) 358–370. [CrossRef] [Google Scholar]
- I. Harari and E. Turkel, Accurate finite difference methods for time-harmonic wave propagation. J. Comput. Phys. 119 (1995) 252–270. [CrossRef] [Google Scholar]
- I. Singer and E. Turkel, High order finite difference methods for the Helmholtz equation. Comput. Meth. Appl. Mech. Eng. 163 (1998) 343–358. [CrossRef] [Google Scholar]
- I. Singer and E. Turkel, Sixth order accurate finite difference schemes for the Helmholtz equation. J. Comp. Acous. 14 (2006) 339–351. [CrossRef] [Google Scholar]
- H. Tal-Ezer and E. Turkel, Iterative Solver for the Exterior Helmholtz Problem. SIAM J. Sci. Comput. 32 (2010) 463–475. [CrossRef] [Google Scholar]
- E. Turkel, Numerical methods and nature. J. Sci. Comput. 28 (2006) 549–570. [CrossRef] [Google Scholar]
- E. Turkel, Boundary Conditions and Iterative Schemes for the Helmholtz Equation in Unbounded Regions, Computational Methods for Acoustics Problems, edited by F. Magoules. Saxe-Coburg Publ. UK (2008). [Google Scholar]
- H.A. van der Vorst, Bi-CGSTAB : A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (1992) 631–644. [CrossRef] [MathSciNet] [Google Scholar]
- M.B. van Gijzen, Y.A. Erlangga and C. Vuik, Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplace precondtioner. SIAM J. Sci. Comput. 29 (2006) 1942–1958. [Google Scholar]
- R. Wienands, C.W. Oosterlee, On three-grid Fourier analysis for multigrid. SIAM J. Sci. Comput. 22 (2001) 651–671. [CrossRef] [Google Scholar]
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