The Pulsed Field Magnetization (PFM) is a compact and fast method to magnetize superconducting bulks compared to the field cooling method. However, the heat generation induced by the strong applied variable magnetic field during the PFM makes high trapped magnetic field harder to achieve. In order to make the REBaCuO bulks easier to magnetize by PFM, superconducting bulks including a superconducting weld are studied taking into account the thermal and electromagnetic properties of the weld different from those of the bulk body. This artificial grain boundary obtained by superconducting welding method might increase the trapped magnetic flux without increasing the applied magnetic field. In this paper, we are modelling the superconducting weld behavior during PFM using a 3D finite element model with the software COMSOL Multiphysics. The simulations are based on an H-formulation from Maxwell's equations and the heat diffusion equation. We analyse the impact of the critical current Jc of the weld on the trapped magnetic field.