Fast solution of time-harmonic wave-equation for full-waveform inversion

For many full-waveform inversion techniques, the most computationally intensive step is the computation of a numerical solution for the wave equation on every iteration. In the frequency domain approach, this requires the solution of very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we bring out attention specifically to CGMN method for solving PDEs, known for being flexible (i.e. it is able to treat equally acoustic data as well as visco-elastic or more complex scenarios) efficient with respect both to memory and computation time, and controllable accuracy of the final approximation. We propose an improvement for the known CGMN method by imposing a minimal residual condition, which incurs in one extra model vector storage. The resulting algorithm called CRMN enjoys several interesting properties as monotonically nonincreasing behaviour of the norm of the residual and minimal residual, guaranteeing optimal convergence for the relative residual criterion. We discuss numerical experiments both in an isolated PDE solve and also within the inversion procedure, showing that in a realistic scenario we can expect a speedup around 25% when using CRMN rather than CGMN.