The propagation of a hard X-ray beam from a partially coherent synchrotron source is simulated by using the novel method based on the coherent mode decomposition of Gaussian Schell model and wave-front propagation. We investigate how the coherency properties and intensity distributions of the beam are changed by propagation through optical elements. Here, we simulate and analyze the propagation of the partially coherent radiation trans- mitted through an ideal slit. We present the first simulations for focusing partially coherent synchrotron hard X-ray beams using this novel method. And when compared with the traditional method which assumes the source is a totally coherent point source or completely incoherent, this method is proved to be more reasonable and can also demonstrate the coherence properties of the focusing beam. We also simulate the Young's double slit experiment and the simulated results validate the academic analysis.
