  Currently, many ab initio codes are being prepared for exascale computing. A
first and important step is to significantly improve the efficiency of existing
implementations by devising better algorithms that can accomplish the same
tasks with enhanced scalability. This manuscript addresses this challenge for
real-time time-dependent density functional theory in the full-potential
all-electron code exciting, with a focus on systems with reduced
dimensionality. Following the strategy described here, calculations can run
orders of magnitude faster than before. We demonstrate this with the molecules
H$_2$ and CO, achieving speedups between 98 to over 50,000. We also present an
example where conventional calculations would be particularly costly, namely
the inorganic/organic heterostructure of pyridine physisorbed on monolayer
MoS$_2$.
