In most cases the ground state would be used as an initial state in a dynamic study of a many-body electronic structure. In the numerical study with density functional theory, a complete simulation would consist of obtaining the ground state of the system by solving Kohn-Sham equation and propagating the system by solving time-dependent Kohn-Sham equation. Although there have been many libraries which can handle two processes in a unified framework, the employment of mesh adaptivity towards the efficiency of the simulation would make the realization of the algorithm much more complicated. In this talk, based on our library AFEABIC, a unified realization of the simulation of above process would be introduced. Several mathematical and technical issues, as well as our methods, would be introduced.