Numerical Simulation Of Crystal Phasefield Models On General Curved Surfacesby High-order Finite Element Method

The crystal phase field model based on classical density functional theory is widely used to study the microstructure evolution phenomenon of materials.Solving the minimum value of the free energy density functional of the crystal phase field model can obtain the corresponding ordered structure of the material.Since it is a kind of high-order nonlinear variational problem,its analytical solution is difficult to obtain,so numerical solution becomes a more effective method.This paper takes the Landau-Brazovskii model as an example to study the high-precision algorithm of the crystal phase field model on the general curved surfaces.In this paper,the high-order isoparametric surface finite element method is used to discretize in space,the first-order semi-implicit scheme and the second-order Crank-Nicolson scheme are used to discretize in time,and the method is implemented based on FEALPy [23].A large number of numerical experiments show that the high-order method used in this paper can calculate the speckle structure and layered structure on the general curved surfaces,which verifies the effectiveness and accuracy of the high-order surface finite element method.