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• Содержание выпуска •
• Software and Hardware for Distributed Systems and Supercomputers •
• Mathematical Modelling •
Mathematical Modelling
Responsible for the Section: doctor of technical Sciences
Vladimir Gurman, candidate of technical Sciences Sergei Amelkin
On the left: assigned number of the paper, submission date, the number
of A5 pages contained in the paper, and the reference to the full-text
PDF
/r1/pdf.jpg) .
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Article #
8_2022
20
p.
/r1/pdf.jpg)
PDF |
submitted on
28th
Apr 2022 displayed on
website on 21th
June
2022 Vladimir E. Ankudinov, Ilya O.
Starodumov
Approximation of periodic solutions of two-mode phase-field crystal
model
In present paper we consider a mathematical model of
two-mode phase-field crystal (PFC). This
model describes the microscopic evolution and
ordering of matter during crystallization from the homogeneous
phase. The model is represented by a
nonlinear partial differential equation of the tenth
order in space and second order in time. The solution of PFC-model
was performed using the Galerkin
finite-element method. Due to the periodic form
of the numerical solutions of this model, the additional
spatial scale appeared and so this requires
an increased discretization accuracy. The mesh convergence
criteria and discretization parameters for the numerical
solutions is considered, taking into account
the computational complexity of two-mode PFC-model.
The influence of size of finite elements (FE) and their order
of base functions on the approximation of the
solution in FE is considered. The correspondent
numerical solution is devoted to the motion of planar
crystallization front. The optimal sizes of
FEs are determined, and the efficiency of numerical simulations
using various software packages and solvers is compared. (In
Russian).
Key words: crystal phase field method, numerical
calculations, finite
elements, approximation. |
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article citation |
http://psta.psiras.ru/read/psta2022_2_65-84.pdf |
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DOI |
https://doi.org/10.25209/2079-3316-2022-13-2-65-84 |
• Software and Hardware for Distributed Systems and Supercomputers •
• Mathematical Modelling •
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