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 |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Steven Wise, UTK |
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| Abstract: |
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| 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 |
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| Date: | 03 / 20 / 2009 |
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| Time: | 03:35pm - 04:25pm |
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