Abstract:
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.
Key words and phrases:crystal phase field method, numerical calculations, finite
elements, approximation.
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