  In this paper we describe a fast algorithm for generating periodic RVEs of
polycrystalline materials. In particular, we use the damped Newton method from
semi-discrete optimal transport theory to generate 3D periodic Laguerre
tessellations (or power diagrams) with cells of given volumes. Complex,
polydisperse RVEs with up to 100,000 grains of prescribed volumes can be
created in a few minutes on a standard laptop. The damped Newton method relies
on the Hessian of the objective function, which we derive by extending recent
results in semi-discrete optimal transport theory to the periodic setting.
