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

Frequency-domain full-waveform inversion (FWI) is suitablefor long-offset stationary-recording acquisition, since reliablesubsurface models can be reconstructed with a few frequen-cies and attenuation is easily implemented without computa-tional overhead. In the frequency domain, wave modeling isa Helmholtz-type boundary-value problem which requires tosolve a large and sparse system of linear equations per fre-quency with multiple right-hand sides (sources). This systemcan be solved with direct or iterative methods. While the for-mer are suitable for FWI application on 3D dense OBC ac-quisitions covering spatial domains of moderate size, the latershould be the approach of choice for sparse node acquisitionscovering large domains (more than 50 millions of unknowns).Fast convergence of iterative solvers for Helmholtz problemsremains however challenging in high frequency regime due tothe non definiteness of the Helmholtz operator, on one side andon the discretization constraints in order to minimize the dis-persion error for a given frequency, on the other side, hencerequiring efficient preconditioners. In this study, we use theKrylov subspace GMRES iterative solver combined with atwo-level domain-decomposition preconditioner. Discretiza-tion relies on continuous Lagrange finite elements of order 3on unstructured tetrahedral meshes to comply with complexgeometries and adapt the size of the elements to the localwavelength (h-adaptivity). We assess the accuracy, the con-vergence and the scalability of our method with the acoustic3D SEG/EAGE Overthrust model up to a frequency of 20 Hz