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Frequency-domain full-waveform inversion (FWI) is suitable for long-offsetstationary-recording acquisition, since reliable subsurface models can bereconstructed with a few frequencies and attenuation is easily implementedwithout computational overhead. In the frequency domain, wave modeling is aHelmholtz-type boundary-value problem which requires to solve a large andsparse system of linear equations per frequency with multiple right-hand sides(sources). This system can be solved with direct or iterative methods. Whilethe former are suitable for FWI application on 3D dense OBC acquisitionscovering spatial domains of moderate size, the later should be the approach ofchoice for sparse node acquisitions covering large domains (more than 50millions of unknowns). Fast convergence of iterative solvers for Helmholtzproblems remains however challenging in high frequency regime due to the nondefiniteness of the Helmholtz operator, on one side and on the discretizationconstraints in order to minimize the dispersion error for a given frequency, onthe other side, hence requiring efficient preconditioners. In this study, weuse the Krylov subspace GMRES iterative solver combined with a two-leveldomain-decomposition preconditioner. Discretization relies on continuousLagrange finite elements of order 3 on unstructured tetrahedral meshes tocomply with complex geometries and adapt the size of the elements to the localwavelength ($h$-adaptivity). We assess the accuracy, the convergence and thescalability of our method with the acoustic 3D SEG/EAGE Overthrust model up toa frequency of 20~Hz.

Large-scale frequency-domain seismic wave modeling on {\it{h}}-adaptive  tetrahedral meshes with iterative solver and multi-level domain-decomposition  preconditioners