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

• N. Bootland and V. Dwarka and P. Jolivet and V. Dolean and C. Vuik (pdf, bibtex)
  Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems
  Domain Decomposition Methods in Science and Engineering XXVI, editors S.C. Brenner and E. Chung and A. Klawonn and F. Kwok and J. Xu and J. Zou
  Lecture Notes in Computational Science and Engineering book series LNCSE, volume 145, pp. 127-135, Springer, Cham, 2023


• Vandana Dwarka and Cornelis Vuik (pdf)
  Stand-alone Multigrid for Helmholtz Revisited: Towards Convergence Using Standard Components
  https://arxiv.org/abs/2308.13476


• Jinqiang Chen, Vandana Dwarka, and Cornelis Vuik (pdf)
  A matrix-free parallel two-level deflation preconditioner for the two-dimensional Helmholtz problems
  https://arxiv.org/abs/2308.06152


• Jinqiang Chen, Vandana Dwarka, and Cornelis Vuik (pdf)
  A matrix-free parallel solution method for the three-dimensional heterogeneous Helmholtz equation
  https://arxiv.org/abs/2308.06085


• V. Dwarka and C. Vuik (pdf, bibtex)
  Scalable multi-level deflation preconditioning for highly indefinite time-harmonic waves
  Journal of Computational Physics, 469, 111327, 2022


• V. Dwarka and C. Vuik (pdf, bibtex)
  Pollution and accuracy of solutions of the Helmholtz equation: A novel perspective from the eigenvalues
  Journal of Computational and Applied Mathematics, 395, 113549, 2021


• Niall Bootland, Vandana Dwarka, Pierre Jolivet, Victorita Dolean, and Cornelis Vuik (pdf)
  Inexact subdomain solves using deflated GMRES for Helmholtz problems
  https://arxiv.org/abs/2103.17081


• V. Dwarka and C. Vuik (pdf, bibtex)
  Scalable Convergence Using Two-Level Deflation Preconditioning for the Helmholtz Equation
  SIAM Journal of Scientific Computing, 42, pp. A901-A928, 2020


• V. Dwarka and R. Tielen and M. Moller and C. Vuik (pdf)
  Towards Accuracy and Scalability: Combining Isogeometric Analysis with Deflation to Obtain Scalable Convergence for the Helmholtz Equation
  https://arxiv.org/abs/2010.10232


• V. Dwarka and C. Vuik (pdf, bibtex)
  Scalable multi-level deflation preconditioning for the highly indefinite Helmholtz equation
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 20-04, 2020
  ISSN 1389-6520


• V. Dwarka and C. Vuik (pdf, bibtex)
  Scalable Convergence Using Two-Level Deflation Preconditioning for the Helmholtz Equation
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 18-03 2018 ISSN 1389-6520


• D. Lahaye and C. Vuik (pdf, bibtex)
  How to Choose the Shift in the Shifted Laplace Preconditioner for the Helmholtz Equation Combined with Deflation
  Modern Solvers for Helmholtz Problems
  Editors: D. Lahaye and J.M. Tang and C. Vuik
  Birkhauser, Basel, pp. 85-112, 2017


• D. Lahaye and J.M. Tang and C. Vuik (pdf, bibtex)
  Modern Solvers for Helmholtz Problems
  Birkhauser, Geosystems Mathematics, Basel, 2017


• A.H. Sheikh and D. Lahaye and L. Garcia Ramos and R. Nabben and C. Vuik (pdf, bibtex)
  Accelerating the shifted Laplace preconditioner for the Helmholtz equation by multilevel deflation
  Journal of Computational Physics, 322, pp. 473-490, 2016


• H. Knibbe and C. Vuik and C.W. Oosterlee (pdf, bibtex)
  Reduction of computing time for least-squares migration based on the Helmholtz equation by graphics processing units
  Computational Geosciences, 20, pp. 297-315, 2016


• H.P. Knibbe ( thesis) Reduction of computing time for seismic applications based on the Helmholtz equation by Graphics Processing Units
  PhD Thesis
  Delft University of Technology, 2015


• A.H. Sheikh ( thesis) Development of the Helmholtz Solver based on a Shifted Laplace Preconditioner and a Multigrid Deflation technique
  PhD Thesis
  Delft University of Technology, 2014


• H. Knibbe and W.A. Mulder and C. W. Oosterlee and C. Vuik (pdf, bibtex)
  Closing the performance gap between an iterative frequency-domain solver and an explicit time-domain scheme for 3D migration on parallel architectures
  Geophysics, 79, pp. S47-S61, 2014


• A.H. Sheikh and D. Lahaye and C. Vuik (pdf, bibtex)
  On the convergence of shifted Laplace preconditioner combined with multilevel deflation
  Numerical Linear Algebra with Applications, 20, pp. 645-662, 2013


• 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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