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

Bourne, D.P., Pearce, M. and Roper, S.M. (2023) Geometric modelling of polycrystalline materials: Laguerre tessellations and periodic semi-discrete optimal transport. Mechanics Research Communications, 127, 104023. (doi: 10.1016/j.mechrescom.2022.104023)

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.

• Item Type: Articles
• Additional Information: DPB acknowledges financial support from the EPSRC grant EP/V00204X/1. MP thanks the Centre for Doctoral Training in Mathematical Modelling, Analysis and Computation funded by EPSRC grant EP/S023291/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Roper, Dr Steven
• Authors: Bourne, D.P., Pearce, M., and Roper, S.M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mechanics Research Communications
• Publisher: Elsevier
• ISSN: 0093-6413
• ISSN (Online): 1873-3972
• Published Online: 09 December 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Mechanics Research Communications 127: 104023
• Publisher Policy: Reproduced under a Creative Commons License