Preconditioning and multiple-right hand sides strategies for the solution of the frequency-domain wave propagation problem using the CGMN method
Résumé
Frequency-domain waveform modeling in the acoustic and elastic approximations requires the solution of large ill-conditioned linear systems. In the context of frequency-domain full waveform inversion, the solutions of these systems are required for a large number of sources (i.e. right-hand sides). Because of their tremendous memory requirements, direct solvers are not yet adapted to the solution of 3D elastodynamics equations. We are thus interested in the use of efficient iterative solvers adapted to the solution of these systems. The CGMN method has shown robust convergence properties for 2D and 3D elastic problems in highly heterogeneous media, compared to standard Krylov methods, but still requires a large number of iterations to reach sufficient accuracy. In this study, the design of an efficient preconditioning strategy adapted to this method is investigated. This preconditioner is computed as a sparse approximate inverse of a heavily damped wave propagation operator. In addition, the single seed method is used to increase the efficiency of the solver for multiple right-hand sides. The efficiency of these two combined strategies is evaluated on the 2D BP2004 model in the visco-acoustic approximation, up to 40 Hz. An overall time speed-up equal to 3 and a reduction of the number of iterations by a factor 10 are observed.