  In polar semiconductors and oxides, the long-range nature of the
electron-phonon (\textit{e}-ph) interaction is a bottleneck to compute charge
transport from first principles. Here, we develop an efficient ab initio scheme
to compute and converge the \textit{e}-ph relaxation times (RTs) and electron
mobility in polar materials. We apply our approach to GaAs, where using the
Boltzmann equation with state-dependent RTs, we compute mobilities in excellent
agreement with experiment at 250$-$500~K. The $e$-ph RTs and the phonon
contributions to intravalley and intervalley $e$-ph scattering are also
analyzed. Our work enables efficient ab initio computations of transport and
carrier dynamics in polar materials.
