Ultrashort laser interactions with dielectrics are numerically investigated by using a multi-physics approach based on Maxwell's equations coupled with a multiple rate free carrier density equation and with the integrated two-temperature model describing the energy transfer from the conduction band electrons to lattice. The model accounts for a complete Keldysh photoionization rate, impact ionization rate and recombination processes typical for glasses, such as fused silica, as well as for the local field enhancement around nanodefects of different size and density. The model allows us not only to study the electron kinetics during the single laser pulse duration but also the accumulation processes, which take place between the pulses giving a rise to nonlinear ionization memory phenomenon in the case of multiple irradiation of transparent solids.