  Primordial gravitational waves provide a very important stochastic background
that could be detected soon with interferometric gravitational wave antennas or
indirectly via the induced patterns in the polarization anisotropies of the
cosmic microwave background. The detection of these waves will open a new
window into the early Universe, and therefore it is important to characterize
in detail all possible sources of primordial gravitational waves. In this paper
we develop theoretical and numerical methods to study the production of
gravitational waves from out-of-equilibrium gauge fields at preheating. We then
consider models of preheating after hybrid inflation, where the symmetry
breaking field is charged under a local U(1) symmetry. We analyze in detail the
dynamics of the system in both momentum and configuration space, and show that
gauge fields leave specific imprints in the resulting gravitational wave
spectra, mainly through the appearence of new peaks at characteristic
frequencies that are related to the mass scales in the problem. We also show
how these new features in the spectra correlate with string-like spatial
configurations in both the Higgs and gauge fields that arise due to the
appearance of topological winding numbers of the Higgs around Nielsen-Olesen
strings. We study in detail the time evolution of the spectrum of gauge fields
and gravitational waves as these strings evolve and decay before entering a
turbulent regime where the gravitational wave energy density saturates.
