Brian Wetton: Numerical methods for energy gradient flows from materials science models

Numerical methods are considered for partial differential equations describing structural evolution in some materials science models. The models are characterized by an energy gradient flow. Examples considered are the Allen-Cahn, Cahn-Hilliard and Functionalized Cahn-Hilliard equations. Basic ideas in spatial and temporal discretization are described, with application to these problems. Sample MATLAB codes for benchmark problems and references to more advanced material will be given. In certain limits of these equations, interfaces moving with certain geometric motions are found. As a final topic, numerical methods for computing these interface motions directly are discussed. Topics by lecture:

1. Introduction and spatial discretization (Finite Difference/Volume, Finite Element, Spectral)
2. Time stepping and the solution of the systems arising from implicit schemes
3. Adaptive strategies
4. Methods for geometric motion of interfaces

Lecture notes
Matlab code (Ch 1)
Matlab code (Ch 2)