Contemporary interest in full waveform inversion (FWI) drives development of 3D forward modeling algorithms. Performing FWI in the frequency domain effectively reduces an inverse problem to the series of monochromatic forward simulations. Still, forward modeling consumes bulk of the FWI run time. In this paper, we focus on efficient solution of the acoustic-wave equation. The most time-consuming step in numerical solution of the acoustic-wave equation is iterative solution of the arising system of linear equations. A slow convergence of iterative solvers is related to the spectral properties of the system matrix [ ]. Consequently, various preconditioning techniques were applied to this kind of problems.


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  1. Abubakar, A, Habashy, T.M.
    [2013], Three-dimensional visco-acoustic modeling using a renormalized integral equation iterative solver, J. Comput. Phys, 249: 1–12.
    [Google Scholar]
  2. Ernst, O.G., Gander, M.J.
    [2012], Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods, Numerical Analysis of Multiscale Problems. Lecture Notes in Computational Science and Engineering, 83.
    [Google Scholar]
  3. BelonosovM., Dmitriev, M., Kostin, V., Neklyudov, D., & TcheverdaV.
    [2017], An iterative solver for the 3D Helmholtz equation, J. Comput. Phys, 345, 330–344.
    [Google Scholar]
  4. Berenger, J. P.
    , [1994] A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys, 114: 185–200.
    [Google Scholar]
  5. Erlangga, Y.A., Vuik, C., & Oosterlee, C.W.
    [2004] On a class of preconditioners for solving the Helmholtz equation, App. Num. Math.50: 409–425.
    [Google Scholar]
  6. Frigo, M. and Johnson, S. G.
    [2005], The Design and Implementation of FFTW3, Proceedings of the IEEE93 (2): 216–231.
    [Google Scholar]
  7. Plessix, R.-E. and Mulder, W.A.
    [2003], Separation-of-variables as a preconditioner for an iterative Helmholtz solver, App. Num. Math, 44: 385–400.
    [Google Scholar]
  8. Yavich, N. and Zhdanov, M.S.
    [2016], Contraction pre-conditioner in finite-difference electromagnetic modeling, Geophys. J. Int, 206 (3): 1718–1729.
    [Google Scholar]
  9. Zhdanov, M. S.
    [2002]. Geophysical inverse theory and regularization problems, Elsevier.
    [Google Scholar]

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