A semi|analytical Fourier spectral method for the Allen

A semi|analytical Fourier spectral method for the Allen–Cahn equation

A semi-analytical Fourier spectral method for the Allen–Cahn equation

We present a first and a second order semi-analytical Fourier spectral (SAFS) methods for solving the Allen–Cahn equation.

A semi-analytical Fourier spectral method for the Allen–

The temporal and spatial evolution of the order parameters is governed by the Cahn–Hilliard equation. [2–10] or the Allen–Cahn (AC) equation [11 ...

A semi-analytical Fourier spectral method for the Allen-Cahn equation

Abstract. In recent years, Fourier spectral methods have been widely used as a powerful tool for solving phase-field equations. To improve its effectiveness, ...

Computers and Mathematics with Applications a Semi-analytical ...

A first and a second order semi-analytical Fourier spectral (SAFS) methods for solving the Allen-Cahn equation, which decompose the original equation into ...

A semi-analytical Fourier spectral method for the Allen–Cahn equation

List of references · Yang, Error analysis of stabilized semi-implicit method of Allen–Cahn equation, Discrete Contin. Dyn. Syst. Ser. B, № 11, с. 1057 · Fife, ...

A semi-analytical Fourier spectral method for the Swift–Hohenberg ...

The SH equation is a fourth-order nonlinear partial differential equation and cannot generally be solved analytically. Therefore, computer simulations play an ...

A semi-analytical Fourier spectral method for the Allen-Cahn ...

Engineering · Numerical Experiment · Powerful Tool · Phase Field · Field Equation · Explicit Scheme · Fourier Space · Closed Form Solution · Phase Separation ...

Fourier-Spectral Method for the Phase-Field Equations - MDPI

In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field ...

Implementing semi-implicit Fourier spectral method - Julia Discourse

I'm trying to implement the semi-implicit Fourier spectral method described here. It is basically a fourth-order phase-field equation.

Asymptotically Compatible Fourier Spectral Approximations of ...

We study Fourier spectral approximations of a nonlocal Allen--Cahn (NAC) equation that reduces to the conventional Allen--Cahn equation in the local limit.

PlaneWaves.ipynb - cortner/JuliaTutorials - GitHub

In the next example, we implement a spectral method for the Allen--Cahn equation, u t = ϵ u x x − 1 ϵ ( u 3 − u ) , again supplemented with PBCs and a random ...

Higher order operator splitting Fourier spectral methods for the Allen ...

Abstract:The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator ...

Applications of semi-implicit Fourier-spectral method to phase field ...

Elliot, Kinetics of phase decomposition processes: Numerical soutions to Cahn-Hilliard equation,. Mater. Sci. & Technol. 6 (1990) 273–283. [15] S.M. Allen, J.W. ...

Asymptotically Compatible Fourier Spectral Approximations of ...

We study Fourier spectral approximations of a nonlocal Allen–Cahn (NAC) equation that reduces to the conventional Allen–Cahn equation in the local limit. We ...

(PDF) Fourier-Spectral Method for the Phase-Field Equations

PDF | In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg ...

Fourier Spectral High-Order Time-Stepping Method for Numerical ...

Several numerical experiments are carried out on multi-dimensional Allen–Cahn equations including a two-dimensional Allen–Cahn equation with a radially ...

Fourier spectral high-order time-stepping method for numerical ...

Allen and Cahn studied the anti-phase boundaries in binary alloys to discover topical changes by creating a phase-field model. These equations ...

[PDF] Fourier-Spectral Method for the Phase-Field Equations

In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field ...

Numerical Approximations of Allen-Cahn and Cahn-Hilliard Equations.

Most of the analysis are for finite element/finite difference methods or. Fourier-spectral method with periodic boundary conditions. Very few work has been ...

Fourier Spectral High-Order Time-Stepping Method for Numerical ...

In this talk, I will present the Fourier spectral method combined with the strongly stable exponential time difference method as an ...