Frequency‐domain full‐waveform modeling using a hybrid direct‐iterative solver based on a parallel domain decomposition method: A tool for 3D full‐waveform inversion?

We present a parallel domain decomposition method for frequency‐domain modeling of wave propagation. The domain decomposition method, based on the Schur complement method, uses an hybrid direct‐iterative solver. The main interest of mixing solvers is to overcome the huge memory complexity of direct solvers while partially preserving the efficiency of multi‐RHS simulations and mitigate the iteration count in iterative solvers. To improve the convergence rate of the iterative solver, a preconditioning provided by the local assembled Schur complement is used. Discretization of the time‐harmonic wave equation (Helmholtz equation) is based on a parsimonious staggered finite‐difference grid method but the domain decomposition method could apply to any numerical scheme such as finite‐element or finite‐volume methods. We developed this method as a tool for frequency‐domain full‐waveform inversion.