Calculus of Variations and Geometric Measure Theory
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D. Bourne - M. Pearce - S. Roper

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

created by bourne on 25 Jul 2022

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Inserted: 25 jul 2022
Last Updated: 25 jul 2022

Year: 2022

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.


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