  We present multi-dimensional core-collapse supernova simulations using the
Isotropic Diffusion Source Approximation (IDSA) for the neutrino transport and
a modified potential for general relativity in two different supernova codes:
FLASH and ELEPHANT. Due to the complexity of the core-collapse supernova
explosion mechanism, simulations require not only high-performance computers
and the exploitation of GPUs, but also sophisticated approximations to capture
the essential microphysics. We demonstrate that the IDSA is an elegant and
efficient neutrino radiation transfer scheme, which is portable to multiple
hydrodynamics codes and fast enough to investigate long-term evolutions in two
and three dimensions. Simulations with a 40 solar mass progenitor are presented
in both FLASH (1D and 2D) and ELEPHANT (3D) as an extreme test condition. It is
found that the black hole formation time is delayed in multiple dimensions and
we argue that the strong standing accretion shock instability before black hole
formation will lead to strong gravitational waves.
