We consider the propagation of a front in a given velocity field using marker points. We make a multiresolution decomposition of the front based on subdivision and wavelet offsets. Instead of tracking the markers we track the wavelet offsets, which, like the markers, satisfy ODEs. We show that the finer the spatial scale, the slower the wavelet offsets evolve. By designing a numerical ODE method which uses longer time steps for finer spatial scales we are able to track the front 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 $\Delta t$.
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