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Colloquium of Olof Runborg. Title: Fast Interface Tracking Using Multiresolution Representations of Curves and Surfaces

Event Type: 
Colloquium
Speaker: 
Prof. Olof Runborg
Event Date: 
Thursday, April 17, 2014 -
3:30pm to 4:30pm
Location: 
SMLC 356
Audience: 
General PublicFaculty/StaffStudentsAlumni/Friends
Sponsor/s: 
Mohammad Motamed

Event Description: 

We consider numerical simulations of an interface moving in a
given velocity field. To describe the interface we use a multiresolution
decomposition in which the interface is represented by a set of wavelet
vectors. Instead of tracking marker points on the interface, as in
standard interface tracking methods, we track the wavelet vectors. Like
the markers they satisfy ordinary differential equations. We show that the
finer the spatial scale, the slower the wavelet vectors evolve. By
designing a numerical method which takes longer time steps for finer
spatial scales we are able to track the interface with the same overall
accuracy as when directly tracking the markers, but at a computational
cost of O(log N/Delta t) rather than O(N/Delta t) for N markers and
timestep Delta t. In the talk we will also discuss adaptivity techniques
for nonsmooth and/or rapidly expanding interfaces, as well as an
application of the method to time upscaling of Hamilton-Jacobi equations.


Event Contact

Contact Name: Mohammad Motamed