On the discretization of problems involving periodic planar tilings

Features related to the discretization of problems characterized by simple periodic tilings using cells of various shapes are discussed. Various cell geometries that tile the plane periodically are considered. Equivalent prob lems are identified, where the discretization can take place on a parallelo gram, regardless of the shape of the original cell. These equivalent proble ms also suggest a numbering of the equations that results in matrices with interesting and useful properties. Copyright (C) 2001 John Wiley & Sons, Lt d.