Department of Mathematics

Speaker: Steven Wise
Title: A Convergent, Energy Stable, and Efficient Hexagonal Finite Difference Scheme for the Phase Field Crystal Amplitude Expansion Model
Affiliation: The University of Tennessee, Knoxville
Date: Tuesday, March 15, 2016
Place and Time: Room 201, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. The phase field crystal model is a sixth order, nonlinear parabolic PDE describing crystal dynamics at the atomic length scale, but on diffusion time scales. It can describe point defects, grain boundaries, and elastically mediated phase transformations. I will describe a reformulation of the model using the technique of amplitude expansions, which reduces the model to a system of fourth-order equations, but introduces several complexities. I will briefly describe some properties of the PDE solutions and will then investigate an energy stable and convergent numerical method for the amplitude model based on a non-standard finite difference discretization of space. I will show a number of numerical examples demonstrating the advantages of the scheme. This is joint work with Zhen Guan, Vili Heinonen, John Lowengrub, and Cheng Wang.