RESUMEN: Diblock copolymers self-assemble into a variety of periodic nano-structures in the bulk. The length scale is dictated by the molecular extension and ranges from 10 nm to 100nm. The application of copolymer materials have attracted abiding interest for templating nano-structures in microelectronics and catalysis. If the copolymer material is in contact with a patterned surface, the morphology of the diblock copolymer may either replicate the surface pattern without defects over large areas or a more complex reconstruction of the soft morphology at the patterned surface occurs depending on the mismatch between the symmetry and length scale of surface pattern and bulk morphology. Certain irregular patterns that do not have an analogue in the bulk phase diagram, can be replicated by the adding "defectants" to the copolymer material. These are substances;e.g., homopolymers or nanoparticles; enrich at locations, where the substrate pattern deviates from the bulk morphology, and thereby reduce the excess free-energy of these local structures, permitting defect-free replication. Using computer simulation of soft, coarse-grained polymer models, we investigate the directed assembly of copolymer materials on various surface patterns. The model allows us to investigate large, three-dimensional systems with an experimentally relevant degree of polymerization by computer simulations. Special methods for computing free-energy differences of self-assembled morphologies and grain-boundaries will be discussed and applied to block copolymers in thin films. The computer simulation provides a wealth of information about the three-dimensional structure, its free energy, and also about the kinetics of structure formation.