PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng, Kris Jenssen.

Title:Energy Stable and Convergent Schemes for the Phase Field Crystal (PFC) and Modified Phase Field Crystal (MPFC) Equations
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Steven Wise, UTK
Abstract:
The PFC and MPFC equations model crystals at the atomic scale in space but on diffusive scales in time. These are sixth-order nonlinear PDEs of parabolic and hyperbolic type, respectively. (The MPFC equation is similar in structure to the perturbed viscous Cahn-Hilliard equation, and our methods are applicable to this latter equation as well.) The models accounts for the periodic structure of a crystal lattice through a free energy functional of Swift-Hohenberg type that is minimized by periodic functions. They naturally incorporate elastic and plastic deformations, multiple crystal orientations and defects and have already been used to simulate a wide variety of crystalline microstructures. In this talk I describe energy stable and convergent ?nite di?erence schemes and their e?cient solution using a nonlinear multigrid method. A key point in the numerical analysis is the convex splitting of the functional energy corresponding to the gradient systems. In more detail, the physical energy in both cases can be decomposed into purely convex and concave parts. The convex part is treated implicitly, and the concave part is updated explicitly in the numerical schemes. The proposed schemes are unconditionally stable in terms of their respective energies and unconditionally solvable, properties which allow for arbitrarily large time step sizes. This last aspect is vital for coarsening studies that require very large time scales.

Room Reservation Information

Room Number:MB106
Date:03 / 20 / 2009
Time:03:35pm - 04:25pm