|Date:||Wed, March 23, 2011|
|Place:||IRC East Wing Seminar Room|
Abstract: We consider the numerical simulation of an interface moving in 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/Δt) rather than O(N/Δt) for N markers and timestep Δt. We sketch the proof of this and show numerical examples supporting the theory. We also consider extensions to higher dimensions.