Fast interface tracking via a multiresolution representation of curves and surfaces

Abstract

We consider the propagation of an interface in a velocity field. The initial interface is described by a normal mesh [Guskov, et al, SIGGRAPH Proc., 259-268, 2000] which gives us a multiresolution decomposition of the interface and the related wavelet vectors. Instead of tracking marker points on the interface we track the wavelet vectors, which like the markers 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(logN/Δt) rather than O(N/Δt) for N markers and timestep Δt. We prove this rigorously and give numerical examples supporting the theory. We also consider extensions to higher dimensions and co-dimensions. © 2009 International Press.