One way to study the effects of electron excitation (e.g.photoemission) is to use the Green's function formalism of a many-bodyperturbation theory. In this approach, the effect of excitation isdescribed in terms of quasi-particle energies (eigenvalues) of asingle-particle Hamiltonian that contains a self-energy term used toproperly describe the many-body excitation effects. Thesequasi-particle energies form the poles of a Green's function thatdescribes the probability amplitude to detect an electron (or hole) ata spatial location and certain time when an electron (or hole) hasbeen added to the system at another location and time. The exact formof the self-energy is unknown. A widely used technique to approximatethe self-energy is to express it as the product of an one-particleGreen's function (G) and a screened Coulomb operator (W) in the timedomain. The construction of such an approximation is extremelycomputational demanding.  We will describe a number of techniques forreducing the computational cost for a full-frequency GW calculation.