Dependence on the number of post-smoothing iterations of the occurrence of negative populations at the coarsest grid. The left-hand columns show the relative error at the finest grid after two full V-cycles. The right-hand columns show the relative change of the population at the coarsest grid in a single grid point in the atmosphere. Red dots indicate positive populations; blue dots negative populations. The chosen grid point is indicated by the black dot in the left-hand columns. For each row of panels, a different number of post-smoothing iterations is applied. First row: ν2 = 2; second row: ν2 = 10; third row: ν2 = 20. In the fourth row, we show the relative change of the population at the coarsest grid with ν2 = 2, but we solve Eq. (4) instead of Eq. (10), that is, we perform standard MALI iterations instead of coarse-grid iterations. The computation was performed in a 1D plane-parallel atmosphere constructed from column x = 0, y = 244 of Model 1, with the H i atom. The other multigrid parameters are ν1 = 2, ν3 = 32, full-weighting restriction and linear interpolation.
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