Towards a robust geometric multigrid scheme for Helmholtz equation

We discuss an improvement of existing multigrid techniques for the solution of the time harmonic wave equation targeting application to seismic inversion and imaging, using non-traditional smoothing and coarse correction techniques, namely the CGMN and CRMN methods. We aim at developing a multigrid scheme to be used as a preconditioner for FGMRES showing less sensibility to changes in the discretization of the operator. We compare this multigrid scheme with recent developments in the multigrid field obtaining very satisfactory results. Our numerical experiments using SEG/EAGE Overthrust velocity model showing not only more robustness when switching from a basic 7 points stencil to a more compact 27 points stencil, but also a considerable reduction in the number of preconditioning steps required to attain convergence, a result encouraging further investigation.