Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport

TL;DR

This paper presents a fast algorithm leveraging semi-discrete optimal transport theory to generate large, complex 3D periodic Laguerre tessellations for polycrystalline materials, enabling efficient RVE creation.

Contribution

It introduces a novel damped Newton method for generating periodic Laguerre tessellations with prescribed cell volumes, extending semi-discrete optimal transport to periodic settings.

Findings

Able to generate up to 100,000 grains in minutes

Uses Hessian of the objective function for efficient computation

Extends semi-discrete optimal transport to periodic tessellations

Abstract

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.