In this talk we discuss Helmholtz solvers for frequency domain seismic modelling, imaging and inversion. In such computations typically the same equation is solved for many right hand sides. Recently the author and others have developed methods with (near-) linear cost per solve. So far these methods are memory intensive. We will address this using an optimised multigrid method. In the new method key calculations are done at very coarse grids, with grid sampling close to the Nyquist limit for the oscillatory solutions. This leads to a substantial reduction of the memory use and the computational cost.