Finite Element Methods for Surface Diffusion and Applications to Stressed Epitaxial Films
Ricardo Nochetto
University of Maryland, Department of Mathematics;
and University of Maryland Institute for Physical Science and Technology
Tuesday, May 4, 2004 15:00-16:00,
NIST North (820), Room 145
Gaithersburg
Tuesday, May 4, 2004 13:00-14:00,
Room 4550
Boulder
Abstract:
The overall goal of this project is to devise efficient numerical tools for simulating morphological changes in stressed epitaxial
films and thereby study their complicated nonlinear dynamics.
In fact, to release stress due to misfit with the substrate, atoms on the free surface of the film may diffuse along and yield large
deformations (surface diffusion), including splitting and merging.
Surface diffusion is a 4th order (highly nonlinear) geometric driven motion of a surface with normal velocity proportional to
the surface Laplacian of mean curvature.
We present a novel variational formulation for parametric surfaces which is semi-implicit, requires no explicit parametrization,
and yields a linear system of lower order elliptic partial differential equations to solve at each time step.
We develop a finite element method (FEM), which conserves volume, and propose a Schur complement approach
to solve the resulting linear systems.
We then couple surface diffusion with elasticity in the bulk via a variational approach involving FEM.
We present several numerical experiments for surface diffusion including pinch-off in finite time and topological changes.
We also present preliminary computations for the coupled system which show formation of dislocations.
We discuss time and space adaptivity to handle the multiscale nature of this problem, as well as mesh generation,
mesh distortion, and mesh smoothing.
This work is joint with P. Morin (Argentina) and E. Baensch (Germany).
Speaker Bio:
Ricardo Nochetto received his PhD in Mathematics from the Universidad de Buenos Aires, Buenos Aires, Argentina, in 1983.
Since 1987 he has been a professor in the Department of Mathematics at the University of Maryland, College Park.
In addition, he has held a visiting position at the Institute for Physical Science and Technology since 1992.
His research interests include finite element methods for free boundary problems and phase transitions.
He received the SIAM Outstanding Paper Prize in 2001 and serves as Associate Editor of several publications including
Computational Methods in Applied Mathematics and the SIAM Journal on Numerical Analysis.
Presentation Slides: PDF
Contact: P. M. KetchamNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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