  This paper describes how to efficiently solve time-dependent x-ray dynamic
diffraction problems in distorted crystals with an FFT-based beam propagation
method (FFT BPM). We show examples of using the technique to simulate the
propagation of x-ray beams in deformed crystals in space and time domains
relevant to the cavity-based x-ray Free Electron Lasers (CBXFELs) and XFEL
self-seeding systems.
