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The faceted growth of silicon crystals from the melt is examined by numerical simulation. The numerical model takes into account the attachment kinetics to the different facets of the silicon crystal. It calculates the macroscopic shape of a single crystal, that is dominated by the low index planes, as well as the competition between crystals with different crystallographic orientations. The model is applied to the directional growth of multicrystalline silicon from the melt. The grain selection is discussed with respect to the crystallographic orientation of the different grains. The numerical model can be applied to many different growth techniques in order to study the dependency of the crystalline structure on the process conditions. It is easily transferable to other growth techniques like epitaxial growth from the liquid or from the gas phase.