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Numerical-methods-for-the-Cahn-Hilliard-equation

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Numerical schemes for the Cahn-Hilliard equation.

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CH2D11.m
CH2D12.m
CH2D13.m
CH2D14.m
CH2D15.m
CH2D_Plot_Evolution.m
CH_intial_2D.m
dcircle.m
ddiff.m
distmesh2d.m
drectangle.m
Energy_2D.m
Example_Script.m
FEM_Cahn_Hilliard_Irregular.m
FEM_Cahn_Hilliard_Rectangular.m
fixmesh.m
Generate_2D_Matrices.m
Generate_2D_Simulations.m
Generate_Irregular_FEM_Mesh.m
Generate_Large_2D_Simulations.m
Generate_Rect_Mesh.m
huniform.m
localf.m
localJ.m
Mass_2D.m
README.md
simpplot.m
simpvol.m
Time_2D_Schemes.m

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This repository is based on the paper "Numerical Methods for the Cahn-Hilliard Equation", by Matthew Geleta, submitted as part of an MSc degree in Mathematics at The University of Oxford.

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Run the script "Example_Script.m" for a demonstration of the finite difference solver, and a pretty simulation.

Run the script "FEM_Cahn_Hilliard_Irregular.m" to view a finite element solution to the stead-state
Cahn-Hilliard equation on an irregular domain.

Run the script "FEM_Cahn_Hilliard_Rectangular.m" to view a finite element solution to the stead-state
Cahn-Hilliard equation on a rectangular domain.
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This repository includes MATLAB code for:
-Five finite-difference schemes for the two-dimensional Cahn-Hilliard equation with Neumann boundary conditions.
-A finite element scheme for the steady-state Cahn-Hilliard equation.
-Functions to compute area integrals using a two-dimensional Simpson's rule.
-Functions to generate animations showing the evolution of the Cahn-Hilliard system.
-An example script (called "Example_Script") to demonstrate how the finite-difference code works.
-Some background dependency files called internally within some functions.