Creat membership Creat membership
Sign in

Forgot password?

Confirm
  • Forgot password?
    Sign Up
  • Confirm
    Sign In
Creat membership Creat membership
Sign in

Forgot password?

Confirm
  • Forgot password?
    Sign Up
  • Confirm
    Sign In
Collection

toTop

If you have any feedback, Please follow the official account to submit feedback.

Turn on your phone and scan

home > search >

Comparison study of numerical methods for solving the Allen–Cahn equation

Author:
Jeong, Darae   Lee, Seunggyu   Lee, Dongsun   Shin, Jaemin   Kim, Junseok  


Journal:
Computational Materials Science


Issue Date:
2016


Abstract(summary):

Highlights

We present a critical comparison for solving the Allen–Cahn equation.

Numerical solvability and stability are discussed.

We show the pointwise boundedness of the numerical solution.

We demonstrate its usefulness with the numerical experiments.

Abstract

The goal of this paper is to present a brief review and a critical comparison of the performance of several numerical schemes for solving the Allen–Cahn equation representing a model for antiphase domain coarsening in a binary mixture. Explicit, fully implicit, Crank–Nicolson, and unconditionally gradient stable schemes are considered. In this paper, we show the solvability conditions of the numerical schemes and the decreasing property of total energy using eigenvalues of the Hessian matrix of the energy functional. We also present the pointwise boundedness of the numerical solution for the Allen–Cahn equation. To compare the accuracy and numerical efficiency of these methods, numerical experiments such as traveling wave and motion by mean curvature are performed. Numerical results show that Crank–Nicolson and nonlinearly stabilized splitting schemes are almost close to the analytic solution. However, if a large time step is used in the numerical test, we have only two results with linearly and nonlinearly stabilized splitting schemes in spite of having large gaps between analytic solution and numerical results. The other numerical schemes except for linearly and nonlinearly stabilized splitting schemes have unstable results when large time step is used.

Graphical abstract

Numerical traveling wave solutions with an initial profile View the MathML source and two different time step sizes at final time T=140h2 . (a) and (b) are results with Δt=0.1h2 and 10h2, respectively.



Page:
131-136


Similar Literature

Submit Feedback

This function is a member function, members do not limit the number of downloads