Minimal-residual iterative methods for time-harmonic wave-equation

In this work we aim at comparing the performance of some iterative methods for solving the time-harmonic acoustic wave-equation, one of the most challenging problems in the numerical linear algebra community. Widely used in frequency domain full waveform inversion, the discrete wave-equation yields very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we aim at further comparing our recently proposed method, CRMN, against CGMN and another method renown for being very memory efficient, the two-level preconditioner with shifted Laplacian operator. We propose several improvements for the two-level preconditioner by combining this method with CRMN in several senses.