We present a set of cosmological simulations with radiative transfer in orderto model the reionization history of the Universe. Galaxy formation and theassociated star formation are followed self-consistently with gas and darkmatter dynamics using the RAMSES code, while radiative transfer is performed asa post-processing step using a moment-based method with M1 closure relation inthe ATON code. The latter has been ported to a multiple Graphics ProcessingUnits (GPU) architecture using CUDA + MPI, resulting in an overall acceleration(x80) that allows us to tackle radiative transfer problems at resolution of1024^3 + 2 levels of refinement for the hydro adaptive grid and 1024^3 for theRT cartesian grid. We observe a good convergence between our differentresolution runs as long as the effects of finite resolution on the starformation history are properly taken into account. We also show that theneutral fraction depends on the total mass density, in a way close to thepredictions of photoionization equilibrium, as long as the effect ofself-shielding is included in the background radiation model. However we stillfail at reproducing the z=6 constraints on the H neutral fraction and theintensity of the UV background. In order to account for unresolved densityfluctuations, we added a simple clumping factor model. Using our most spatiallyresolved simulation (12.5 Mpc/h-1024^3) to calibrate our subgrid model, we haveresimulated our largest box (100 Mpc/h 1024^3), successfully reproducing theobserved level of H neutral fraction at z=6. We don't reproduce thephotoionization rate inferred from the same observations. We argue that thisdiscrepancy could be explained by the fact that the average radiation intensityand the average neutral fraction depends on different regions of the gasdensity distribution, so that one quantity cannot be simply deduced from theother.
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