Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method

1999 ◽  
Vol 60 (4) ◽  
pp. 3564-3572 ◽  
Author(s):  
Jingzhi Zhu ◽  
Long-Qing Chen ◽  
Jie Shen ◽  
Veena Tikare
Keyword(s):  
Spectral Method ◽  
Fourier Spectral Method ◽  
Hilliard Equation ◽  
Coarsening Kinetics ◽  
Cahn Hilliard Equation

The Fourier spectral method for the Cahn–Hilliard equation

2005 ◽  
Vol 171 (1) ◽  
pp. 345-357 ◽  
Author(s):  
Xingde Ye ◽  
Xiaoliang Cheng
Keyword(s):  
Spectral Method ◽  
Fourier Spectral Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals A Fourier spectral method for fractional-in-space Cahn–Hilliard equation

2017 ◽  
Vol 42 ◽  
pp. 462-477 ◽  
Author(s):  
Zhifeng Weng ◽  
Shuying Zhai ◽  
Xinlong Feng
Keyword(s):  
Spectral Method ◽  
Fourier Spectral Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals A Stabilized Fourier Spectral Method for the Fractional Cahn-Hilliard Equation

2018 ◽  
Vol 1 (3) ◽  
Author(s):  
Liquan Mei
Keyword(s):  
Spectral Method ◽  
Numerical Experiments ◽  
Second Order ◽  
Fourier Spectral Method ◽  
Numerical Schemes ◽  
Hilliard Equation ◽  
Discretization Schemes ◽  
Energy Stable ◽  
Cahn Hilliard Equation ◽  
Crank Nicolson

In this paper, the second order accurate (in time) energy stable numerical schemes are presented for the Fractional Cahn-Hilliard (CH) equation. Combining the stabilized technique, we apply the implicit Crank-Nicolson formula (CN) to derive second order temporal accuracy, and we use the Fourier spectral method for space discrete to obtain the fully discretization schemes. It is shown that the schemes are unconditionally energy stable. A few numerical experiments are presented to conclude the article.

scholarly journals Curve and Surface Smoothing Using a Modified Cahn-Hilliard Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yongho Choi ◽  
Darea Jeong ◽  
Junseok Kim
Keyword(s):  
Piecewise Linear ◽  
Three Dimensional ◽  
Computational Results ◽  
Fourier Spectral Method ◽  
Splitting Scheme ◽  
Surface Smoothing ◽  
Three Dimensional Objects ◽  
Hilliard Equation ◽  
Stable Splitting ◽  
Cahn Hilliard Equation

We present a new method using the modified Cahn-Hilliard (CH) equation for smoothing piecewise linear shapes of two- and three-dimensional objects. The CH equation has good smoothing dynamics and it is coupled with a fidelity term which keeps the original given data; that is, it does not produce significant shrinkage. The modified CH equation is discretized using a linearly stable splitting scheme in time and the resulting scheme is solved by using a Fourier spectral method. We present computational results for both curve and surface smoothing problems. The computational results demonstrate that the proposed algorithm is fast and efficient.

scholarly journals The Spectral Method for the Cahn-Hilliard Equation with Concentration-Dependent Mobility

2012 ◽  
Vol 2012 ◽  
pp. 1-35 ◽  
Author(s):  
Shimin Chai ◽  
Yongkui Zou
Keyword(s):  
Theoretical Analysis ◽  
Convergence Analysis ◽  
Spectral Method ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Type Equation ◽  
Euler Method ◽  
Implicit Euler Method ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

This paper is concerned with the numerical approximations of the Cahn-Hilliard-type equation with concentration-dependent mobility. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method for the space and the implicit Euler method for the time. Numerical experiments are carried out to illustrate the theoretical analysis.

scholarly journals On the sharp interface limit of a model for phase separation on biological membranes

Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Abels ◽  
Johannes Kampmann
Keyword(s):  
Lipid Raft ◽  
Cell Membranes ◽  
System Modeling ◽  
Bulk Diffusion ◽  
Type Equation ◽  
Sharp Interface ◽  
Interface Problem ◽  
Hilliard Equation ◽  
System A ◽  
Cahn Hilliard Equation

AbstractWe rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed in [H. Garcke, J. Kampmann, A. Rätz and M. Röger, A coupled surface-Cahn–Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes, Math. Models Methods Appl. Sci. 26 2016, 6, 1149–1189] to weak (varifold) solutions of the corresponding sharp-interface problem for a suitable subsequence. In the system a Cahn–Hilliard type equation on the boundary of a domain is coupled to a diffusion equation inside the domain. The proof builds on techniques developed in [X. Chen, Global asymptotic limit of solutions of the Cahn–Hilliard equation, J. Differential Geom. 44 1996, 2, 262–311] for the corresponding result for the Cahn–Hilliard equation.

Sign in / Sign up

Export Citation Format

Share Document