  Neutrino transport in spherically symmetric models of stellar core collapse
and bounce has achieved a technically complete level, rewarded by the agreement
among independent groups that a multi-dimensional treatment of the
fluid-instabilities in the post-bounce phase is indispensable to model
supernova explosions. While much effort is required to develop a reliable
neutrino transport technique in axisymmetry, we explore neutrino physics
approximations and parameterizations for an efficient three-dimensional
simulation of the fluid-instabilities in the shock-heated matter that
accumulates between the accretion shock and the protoneutron star. We
demonstrate the reliability of a simple parameterization scheme in the collapse
phase and extend our 3D magneto-hydrodynamical collapse simulations to a
preliminary postbounce evolution. The growth of magnetic fields is
investigated.
