An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations

DOI10.1016/j.jcp.2016.06.007zbMath1349.74360OpenAlexW2422912943MaRDI QIDQ727011

Cheng Wang, Zhen Guan, Vili Heinonen, Steven M. Wise, John S. Lowengrub

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.06.007

zbMATH Keywords

multigridamplitude equationsenergy stable schemephase field crystalhexagonal finite differences

Mathematics Subject Classification ID

Crystalline structure (74E15) Statistical mechanics of crystals (82D25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods applied to problems in solid mechanics (74S20)

Related Items (9)

A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance ⋮ A simple and practical finite difference method for the phase-field crystal model with a strong nonlinear vacancy potential on 3D surfaces ⋮ Generalized Allen-Cahn-type phase-field crystal model with FCC ordering structure and its conservative high-order accurate algorithm ⋮ Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation ⋮ High-order time-accurate, efficient, and structure-preserving numerical methods for the conservative Swift-Hohenberg model ⋮ Linear and energy stable schemes for the Swift-Hohenberg equation with quadratic-cubic nonlinearity based on a modified scalar auxiliary variable approach ⋮ A review on computational modelling of phase-transition problems ⋮ Numerical approximation of the square phase-field crystal dynamics on the three-dimensional objects ⋮ The Cahn-Hilliard equation and some of its variants

Cites Work

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• Complete solution to seven-point schemes of discrete anisotropic Laplacian on regular hexagons
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