The project deals with the additive manufacturing technology of selective laser melting, in which a workpiece is built up by melting powder layer by layer using a laser. The manufacturing process is modeled on two levels: On the macro level, the temperature curve and the residual stresses are analyzed, while on the meso level, the powder bed and the melting process of the material are considered. The finite difference method (FDM) is used to simulate these processes. In order to reduce computing time and increase efficiency, the calculation is carried out using graphics processing units (GPUs). This hardware acceleration enables fast and precise execution of the extensive simulations required for a detailed analysis of the processes.