Behavior of the relative error in population at the finest grid during various steps in a V-cycle with three grids, for the FAL-C atmosphere (left-hand panels) and a column extracted from a 3D radiation-MHD atmosphere (atmosphere Model 1, see Sect. 3). Both computations are done for a H i atom using 10 pre-smoothings, 32 coarse-grid iterations and 25 post-smoothings. Upper panel: temperature and electron density in the atmosphere. Lower panels: error for the H in = 2 level after the pre-smoothing (red), the error after application of the coarse-grid correction (blue), and the error after application of the post-smoothing (purple). For both atmospheres the coarse grid correction has decreased the low spatial-frequency error, but increased the high-frequency error. The latter is largely removed by the post-smoothing.
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