The generalized Floquet formalisms have been developed and applied to a wide range of laser-induced chemical and physical processes [Phys. Rep. 390, 1 (2004)]. The non-Hermitian Floquet formalism and complex quasienergy methods provide accurate non-perturbative treatment of bound–continuum processes of strong-field multiphoton phenomena. I have extended the time-independent non-Hermitian Floquet formalism for high-precision calculation of the multiphoton ionization (MPI) rates of H₂⁺ in intense laser fields, employing the generalized pseudospectral method and the complex scaling method [1]. I also have extended the time-dependent non-Hermitian Floquet approach of time-dependent density functional theory (TDDFT) to investigate the one-photon ionization cross sections and the MPI rates of rare gases, where the computational procedure includes the generalized pseudospectral method, the exterior complex scaling method, and non-Hermitian time propagation of the time-evolution operator [2].