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