  Massive sets of stellar spectroscopic observations are rapidly becoming
available and these can be used to determine the chemical composition and
evolution of the Galaxy with unprecedented precision. One of the major
challenges in this endeavour involves constructing realistic models of stellar
spectra with which to reliably determine stellar abundances. At present, large
stellar surveys commonly use simplified models that assume that the stellar
atmospheres are approximately in local thermodynamic equilibrium (LTE). To test
and ultimately relax this assumption, we have performed non-LTE calculations
for $13$ different elements (H, Li, C, N, O, Na, Mg, Al, Si, K, Ca, Mn, and
Ba), using recent model atoms that have physically-motivated descriptions for
the inelastic collisions with neutral hydrogen, across a grid of $3756$ 1D
MARCS model atmospheres that spans $3000\leq
T_{\mathrm{eff}}/\mathrm{K}\leq8000$,
$-0.5\leq\log{g/\mathrm{cm\,s^{-2}}}\leq5.5$, and $-5\leq\mathrm{[Fe/H]}\leq1$.
We present the grids of departure coefficients that have been implemented into
the GALAH DR3 analysis pipeline in order to complement the extant non-LTE grid
for iron. We also present a detailed line-by-line re-analysis of $50126$ stars
from GALAH DR3. We found that relaxing LTE can change the abundances by between
$-0.7\,\mathrm{dex}$ and $+0.2\,\mathrm{dex}$ for different lines and stars.
Taking departures from LTE into account can reduce the dispersion in the
$\mathrm{[A/Fe]}$ versus $\mathrm{[Fe/H]}$ plane by up to $0.1\,\mathrm{dex}$,
and it can remove spurious differences between the dwarfs and giants by up to
$0.2\,\mathrm{dex}$. The resulting abundance slopes can thus be qualitatively
different in non-LTE, possibly with important implications for the chemical
evolution of our Galaxy.
