Tree methods for moving interfaces

Fast adaptive numerical methods for solving moving interface problems are p resented. The methods combine a level set approach with frequent redistanci ng and semi-Lagrangian time stepping schemes which are explicit yet uncondi tionally stable. A quadtree mesh is used to concentrate computational effor t on the interface, so the methods move an interface with N degrees of free dom in O(N log N) work per time step. Efficiency is increased by taking lar ge time steps even for parabolic curvature flows. The methods compute accur ate viscosity solutions to a wide variety of difficult moving interface pro blems involving merging, anisotropy, faceting, and curvature. (C) 1999 Acad emic Press.