Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model

TL;DR

This paper introduces an adaptive mesh algorithm based on a renormalization-group approach to efficiently simulate polycrystalline pattern formation in materials, significantly speeding up computations.

Contribution

It presents a novel hybrid amplitude equation method combining Cartesian and polar decompositions for faster polycrystalline simulations.

Findings

Achieved a three orders of magnitude speedup in 2D polycrystalline domain formation simulations.

Demonstrated the effectiveness of the hybrid amplitude equations approach.

Provided a systematic framework for adaptive mesh computation in phase-field crystal models.

Abstract

We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field crystal model to provide the underlying equations for the complex amplitude of the atomic density field--a quantity that is spatially uniform except near topological defects, grain boundaries and other lattice imperfections. Our algorithm is a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline domain formation in two dimensions.