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Title: Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

Abstract

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.

Authors:
 [1];  [2]
  1. Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, 620000 Ekaterinburg (Russian Federation)
  2. AO NPO MKM, Ilfata Zakirova st. 24, 426000 Izhevsk (Russian Federation)
Publication Date:
OSTI Identifier:
22608265
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1759; Journal Issue: 1; Conference: ICAAM 2016: International conference on analysis and applied mathematics, Almaty (Kazakhstan), 7-10 Sep 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICAL METHODS AND COMPUTING; COMPUTERIZED SIMULATION; CRYSTAL GROWTH; CRYSTALLIZATION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; MODIFICATIONS; NUMERICAL SOLUTION; THREE-DIMENSIONAL CALCULATIONS; THREE-DIMENSIONAL LATTICES

Citation Formats

Starodumov, Ilya, and Kropotin, Nikolai. Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid. United States: N. p., 2016. Web. doi:10.1063/1.4959750.
Starodumov, Ilya, & Kropotin, Nikolai. Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid. United States. https://doi.org/10.1063/1.4959750
Starodumov, Ilya, and Kropotin, Nikolai. 2016. "Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid". United States. https://doi.org/10.1063/1.4959750.
@article{osti_22608265,
title = {Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid},
author = {Starodumov, Ilya and Kropotin, Nikolai},
abstractNote = {We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.},
doi = {10.1063/1.4959750},
url = {https://www.osti.gov/biblio/22608265}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1759,
place = {United States},
year = {Wed Aug 10 00:00:00 EDT 2016},
month = {Wed Aug 10 00:00:00 EDT 2016}
}