Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field

We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schrödinger equation (TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula (RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos (SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation (HHG) in these interaction systems.