  In this study, we combine the ab initio Migdal-Eliashberg approach with the
intermediate representation for the Green's function, enabling accurate and
efficient calculations of the momentum-dependent superconducting gap function
while fully considering the effect of the Coulomb retardation. Unlike the
conventional scheme that relies on a uniform sampling across Matsubara
frequencies - demanding hundreds to thousands of points - the intermediate
representation works with fewer than 100 sampled Matsubara Green's functions.
The developed methodology is applied to investigate the superconducting
properties of three representative low-temperature elemental metals: aluminum
(Al), lead (Pb), and niobium (Nb). The results demonstrate the power and
reliability of our computational technique to accurately solve the ab initio
anisotropic Migdal-Eliashberg equations even at extremely low temperatures,
below 1 Kelvin.
