Polycrystalline materials serve as a basis for much of our current technology and will undoubtedly continue to serve a similar role in the future. Their mechanical properties depend not only on intragranular interactions between various defects, including the distribution of sizes and orientations of the grains, but also interactions with the grain boundaries. Modeling the mechanical behavior of polycrystals has become a standard part of the multiscale treatment of deformation. Currently, polycrystalline simulations are done through crystal plasticity methods, which are often informed through elastically isotropic single-crystal dislocation dynamics studies. These single-crystal studies, however, miss out on crucial effects due to the presence of grain boundaries, and as such, a corrective factor has to be taken when applying the output to higher-scale methods. In addition, these studies are generally done under an assumption of isotropic elasticity, due to the computational expense incurred when including anisotropic calculations. I have developed a Fourier transform-based spectral method that allows for the simulation of the evolution defects, such as dislocations, in heterogeneous systems. This method allows for a more accurate understanding of the interplay between defects and their environment, and will have the capability to determine more accurate constitutive laws for the deformation of polycrystals, to be fed into crystal plasticity models.