An Efficient Algorithm for Solving the Phase Field Crystal Model
arXiv:physics/0611243 · doi:10.1016/j.jcp.2008.03.012
Abstract
We present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the Phase Field Crystal (PFC) model. This algorithm allows for an arbitrarily large algorithmic time step. As the basis for our analysis of the accuracy of this algorithm, we determine an effective time step in Fourier space. We then compare our calculations with a set of representative numerical results, and demonstrate that this algorithm is an effective approach for the study of the PFC models, yielding a time step effectively 180 times larger than the Euler algorithm for a representative set of material parameters. As the PFC model is just a simple example of a wide class of density functional theories, we expect this method will have wide applicability to modeling systems of considerable interest to the materials modeling communities.
11 pages, 3 figures
References in corpus (9)
- Theory of Phase Ordering Kinetics
- Modeling Elasticity in Crystal Growth
- Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
- Density of kinks after a quench: When symmetry breaks, how big are the pieces?
- Diffuse-interface model for rapid phase transformations in nonequilibrium systems
- Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step
- Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces
- Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation
- Maximally-fast coarsening algorithms
Cited by in corpus (20)
- Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
- Energy Stable and Efficient Finite-Difference Nonlinear Multigrid Schemes for the Modified Phase Field Crystal Equation
- Phase-field modeling of crystal nucleation in undercooled liquids -- A review
- Amplitude expansion of the binary phase field crystal model
- Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
- Exploring the complex world of two-dimensional ordering with three modes
- Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
- Benchmark computations of the phase field crystal and functionalized Cahn-Hilliard equations via fully implicit, Nesterov accelerated schemes
- Efficiency and accuracy of GPU-parallelized Fourier spectral methods for solving phase-field models
- Hybrid-PFC: coupling the phase-field crystal model and its amplitude-equation formulation
- Improved time integration for phase-field crystal models of solidification
- Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids
- A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks
- Uncovering liquid-substrate fluctuation effects on crystal growth and disordered hyperuniformity of two-dimensional materials
- Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions
- Navigating the Complex Landscape of Shock Filter Cahn-Hilliard Equation: From Regularized to Entropy Solutions
- Error analysis of SAV finite element method to phase field crystal model
- Two-level overlapping Schwarz preconditioners with universal coarse spaces for th-order elliptic problems
- A modified Allen-Cahn model for pattern synthesis on surfaces
- A interior penalty method for th-Laplace equation