Annual Report 2008.pdf - SAMSI

efficiently generate solutions with a high order of accuracy. Comparison with the standard level
set reinitialization algorithm shows ours is superior in terms of predictability and local
construction, critical, for example, in local level set methods. We further apply the same ideas to
extension of values off interfaces. Together, our proposed approaches can be used to advance the
level set method for fast and accurate computations of the latest scientific problems.
Jon Wilkening
University of California, Berkeley
Department of Mathematics
wilken@math.berkeley.edu
“Shape Optimization of Swimming Sheets”
Motivated by the propulsion mechanisms adopted by gastropods, we consider shape optimization
of a flexible sheet which propels itself over a thin layer of viscous fluid by propagating
deformation waves along its body. We use a lubrication approximation to model the dynamics
and derive the relevant Euler-Lagrange equations to optimize swimming speed and efficiency.
We present a fast, highly accurate method for solving the optimization equations and explore the
solution in various singular limits. We also monitor the validity of the model using a new
rigorous error estimate for Reynolds' approximation.
Hongkai Zhao
University of California, Irvine
Department of Mathematics
zhao@math.uci.edu
“Grid Based Particle Method for Moving Interface Problem”
We introduce a novel formulation that combines Lagragian particle method with an Eulerian
reference. The interface is represented and tracked with quasi-uniform distributed particles
without mesh or parametrization. Each of the particle is asscociated to an underlying grid point
near the interface and vice versa. Adaptivity is easily acheived through the underlying grid and
simple tree data structure. Topological changes can be controled according to the physics. We
will use extensive numerical examples, such as with given (normal) velocity, mean curvature
flow, surface diffusion of Laplacian and Willmore flow in 2D and 3D to demonstrate our
algorithm.
XV. Program on Environmental Sensor Networks Opening
Schedule
Sunday, January 13, 2008
Radisson Hotel RTP
Overview Tutorials
8:00-9:00 Registration and Continental Breakfast