The indirect excitons in double quantum well structures can appear in the ground state under application of an external electric field along the growth axis. The relatively slow radiative decay rate of the indirect exciton can be enhanced by a magnetic field pointing in the same direction. In this report, we numerically calculate the exciton energy levels in the GaAs-based double quantum well structure as well as optimize parameters of the structure to allow a noticeable increase in the radiative decay rate of the indirect exciton there by application of the magnetic field.