  Frequency-domain full-waveform inversion (FWI) is suitable for long-offset
stationary-recording acquisition, since reliable subsurface models can be
reconstructed with a few frequencies and attenuation is easily implemented
without computational overhead. In the frequency domain, wave modelling is a
Helmholtz-type boundary-value problem which requires to solve a large and
sparse system of linear equations per frequency with multiple right-hand sides
(sources). This system can be solved with direct or iterative methods. While
the former are suitable for FWI application on 3D dense OBC acquisitions
covering spatial domains of moderate size, the later should be the approach of
choice for sparse node acquisitions covering large domains (more than 50
millions of unknowns). Fast convergence of iterative solvers for Helmholtz
problems remains however challenging due to the non definiteness of the
Helmholtz operator, hence requiring efficient preconditioners. In this study,
we use the Krylov subspace GMRES iterative solver combined with a multi-level
domain-decomposition preconditioner. Discretization relies on continuous finite
elements on unstructured tetrahedral meshes to comply with complex geometries
and adapt the size of the elements to the local wavelength ($h$-adaptivity). We
assess the convergence and the scalability of our method with the acoustic 3D
SEG/EAGE Overthrust model up to a frequency of 20~Hz and discuss its efficiency
for multi right-hand side processing.
