Positron sources are critical components of the future lepton colliders projects. This is essentially due to the high luminosity required, orders of magnitude higher than existing ones. In addition,polarization of the positron beam rather expands the physics research potential of the machine by increasing the precision of the measurements and enhancing certain types of interactions. In this framework, the Compton sources for polarized positron production are taken into account where the high energy gamma rays are produced by the Compton scattering and subsequently converted in the polarized electron-positron pairs in a target. The Compton multiple IPs line is proposed as one of the solutions to increase the number of captured positrons. This allows a significant increase in the emitted gamma ray flux impinging on the target. The gamma ray production with the Compton multiple IPs line is simulated and used for polarized positron generation. Later, a capture section based on an adiabatic matching device followed by a pre-injector linac is simulated to capture and accelerate the positron beam. The results obtained are presented and discussed.