A multilevel approach to the evolutionary generation of polycrystalline structures

Abstract

The Poisson-Voronoi tesselation is commonly used as an approximation to the microstructure of polycrystalline material. Although simple, this approximation fails to respect basic physical properties observed empirically, including the generally lognormal distribution of grain sizes. Stochastic approximations such as genetic algorithms can be used to adjust a Poisson-Voronoi tesselation to better reflect such a distribution. We apply techniques from multilevel optimisation to give a new approach to the evolutionary generation of polycrystalline structures, in a way that allows approximation of a target lognormal grain size distribution with unit mean and arbitrary variance. Results obtained through this method indicate almost perfect distribution fitting, show up to two orders of magnitude improvement in the number of evolutionary steps required for an acceptable fit, and suggest a reduction of the overall problem complexity from Θ(<em>N³</em>) to Θ(<em>N³</em>).