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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 2, Pages 213–221 (Mi sjvm473)  

This article is cited in 9 scientific papers (total in 9 papers)

Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics

H. Calandraa, S. Grattonab, R. Lagoca, X. Pinelac, X. Vasseurda

a Centre Scientifique et Technique Jean Féger, Pau, France
b INPT-IRIT, University of Toulouse and ENSEEIHT, Toulouse, France
c Centre Europeen de Recherche et de Formation Avancee en Calcul Scientifique (CERFACS), Toulouse, France
d CERFACS and HiePACS project joint INRIA-CERFACS Laboratory, Toulouse, France
Full-text PDF (213 kB) Citations (9)
References:
Abstract: In this paper we address the solution of three-dimensional heterogeneous Helmholtz problems discretized with compact fourth-order finite difference methods with application to acoustic waveform inversion in geophysics. In this setting, the numerical simulation of wave propagation phenomena requires the approximate solution of possibly very large linear systems of equations. We propose an iterative two-grid method where the coarse grid problem is solved inexactly. A single cycle of this method is used as a variable preconditioner for a flexible Krylov subspace method. Numerical results demonstrate the usefulness of the algorithm on a realistic three-dimensional application. The proposed numerical method allows us to solve wave propagation problems with single or multiple sources even at high frequencies on a reasonable number of cores of a distributed memory cluster.
Key words: flexible Krylov subspace methods, Helmholtz equation, inexact preconditioning, inhomogeneous media.
Received: 17.10.2011
English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 2, Pages 175–181
DOI: https://doi.org/10.1134/S1995423912020127
Bibliographic databases:
Document Type: Article
MSC: 5F10, 65N22, 15A06
Language: Russian
Citation: H. Calandra, S. Gratton, R. Lago, X. Pinel, X. Vasseur, “Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics”, Sib. Zh. Vychisl. Mat., 15:2 (2012), 213–221; Num. Anal. Appl., 5:2 (2012), 175–181
Citation in format AMSBIB
\Bibitem{CalGraLag12}
\by H.~Calandra, S.~Gratton, R.~Lago, X.~Pinel, X.~Vasseur
\paper Two-level preconditioned Krylov subspace methods for the solution of three-dimensional heterogeneous Helmholtz problems in seismics
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
\issue 2
\pages 213--221
\mathnet{http://mi.mathnet.ru/sjvm473}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 2
\pages 175--181
\crossref{https://doi.org/10.1134/S1995423912020127}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862120238}
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  • https://www.mathnet.ru/eng/sjvm473
  • https://www.mathnet.ru/eng/sjvm/v15/i2/p213
  • This publication is cited in the following 9 articles:
    1. Sun D.-L., Carpentieri B., Huang T.-Zh., Jing Ya.-F., “A Spectrally Preconditioned and Initially Deflated Variant of the Restarted Block Gmres Method For Solving Multiple Right-Hand Sides Linear Systems”, Int. J. Mech. Sci., 144 (2018), 775–787  crossref  mathscinet  isi  scopus
    2. Sun D.-L., Carpentieri B., Huang T.-Zh., Jing Ya.-F., Naveed S., “Variants of the Block-Gmres Method For Solving Linear Systems With Multiple Right-Hand Sides”, 2018 International Workshop on Computing, Electromagnetics, and Machine Intelligence (Cemi), ed. Gurel L., IEEE, 2018, 13–14  crossref  mathscinet  isi
    3. D. Lahaye, C. Vuik, Geosystems Mathematics, Modern Solvers for Helmholtz Problems, 2017, 85  crossref
    4. H. Calandra, S. Gratton, X. Vasseur, Geosystems Mathematics, Modern Solvers for Helmholtz Problems, 2017, 141  crossref
    5. Siegfried Cools, Wim Vanroose, Geosystems Mathematics, Modern Solvers for Helmholtz Problems, 2017, 53  crossref
    6. Siegfried Cools, Pieter Ghysels, Wim van Aarle, Jan Sijbers, Wim Vanroose, “A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems”, Journal of Computational and Applied Mathematics, 283 (2015), 1  crossref
    7. Siegfried Cools, Bram Reps, Wim Vanroose, “A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems”, Numer. Linear Algebra Appl., 21:4 (2014), 513  crossref
    8. Sheikh A.H., Lahaye D., Vuik C., “On the Convergence of Shifted Laplace Preconditioner Combined with Multilevel Deflation”, Numer. Linear Algebr. Appl., 20:4, SI (2013), 645–662  crossref  mathscinet  zmath  isi  scopus
    9. Calandra H., Gratton S., Pinel X., Vasseur X., “An Improved Two-Grid Preconditioner for the Solution of Three-Dimensional Helmholtz Problems in Heterogeneous Media”, Numer. Linear Algebr. Appl., 20:4, SI (2013), 663–688  crossref  mathscinet  zmath  isi  scopus
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    Sibirskii Zhurnal Vychislitel'noi Matematiki
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