Numerical Analysis: Fast interface tracking

A multiresolution description of interfaces are used to develop a fast algorithm for their propagation.

In this project we develop fast methods to simulate the propagation of an interface in a velocity field. The interface (a curve or a surface) is described by a multiresolution representation. Instead of tracking marker points on the interface we track wavelet vectors related to the multiresolution description. Like the markers satisfy ordinary differential equations, but 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 that is an order less in the number of unknowns.