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

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

2007-02-07

arxiv.org/abs/cond-mat/0702173v1

Physics

Condensed Matter

Materials Science

37 pages, 15 figures. Submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.76.056706

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.

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