Iterative methods for the Helmholtz equation (Krylov methods, preconditioning, multigrid)

• P.B. Hooghiemstra and D.R. van der Heul and C. Vuik (pdf, bibtex)
  Application of the shifted-Laplace preconditioner for iterative solution of a higher order finite element discretisation of the vector wave equation: First experiences Applied Numerical Mathematics, 60, pp. 1157-1170, 2010


• M. B. van Gijzen, Y. A. Erlangga, and C. Vuik ( pdf , bibtex )
  Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
  SIAM Journal on Scientific Computing, Vol. 29, pp. 1942-1958, 2007
  
  
• C.D. Riyanti and A. Kononov and Y.A. Erlangga and C. Vuik and C. Oosterlee and R.-E. Plessix and W.A. Mulder ( pdf, bibtex)
  A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
  Journal of Computational Physics, 224, pp. 431-448, 2007
  
  
• Y.A. Erlangga and C.W. Oosterlee and C. Vuik ( pdf, bibtex )
  A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
  SIAM J. Sci. Comput.,27, pp. 1471-1492, 2006
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( pdf, bibtex )
  Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation
  Applied Numerical Mathematics, 56, pp. 648-666, 2006
  
  
• C.D. Riyanti and Y.A. Erlangga and R.-E. Plessix and W.A. Mulder and C. Vuik and C. Oosterlee ( pdf, bibtex )
  A new iterative solver for the time-harmonic wave equation
  Geophysics, 71, pp. E57--E63, 2006
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( pdf, bibtex )
  On a robust iterative method for heterogeneous Helmholtz problems for geophysics applications
  International Journal of Numerical Analysis and Modeling, 2, pp. 197--208, 2005
  
  
• Y.A. Erlangga( pdf)
  A robust and efficient iterative method for the numerical solution of the Helmholtz equation
  PhD Thesis, Delft, 2005
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee and R.E. Plessix and W.A. Mulder ( pdf, bibtex )
  A robust iterative solver for the two-way wave equation based on a complex shifted-Laplace operator
  SEG International Exposition and Seventy-Fourth Annual Meeting in Denver, Colorado, October 10-15, 2004
  editor: Society of Exploration Geophysicists International Exposition and Annual Meeting, Society of Exploration Geophysicists, Tulsa, 2004 pages 1897--1900 ISSN 1052-3812
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( pdf, bibtex)
  On a class of preconditioners for solving the Helmholtz equation
  Appl. Num. Math., 50, pp. 409-425, 2004
  
  
• C. Vuik and Y.A. Erlangga and C.W. Oosterlee ( pdf, bibtex)
  Shifted Laplace preconditioners for the Helmholtz equations
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 03-18
  ISSN 1389-6520
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( bibtex)
  On a class of preconditioners for solving the discrete Helmholtz equation
  Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyvaskyla, Finland, 30 June - 4 July, 2003
  editor: G.C. Cohen and E. Heikkola and P. Joly and P. Neittaanmaki, Springer, Berlin, 2003, pages 788-793
  ISBN 3-540-40127-X
  
  

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