A fast modular semi-Lagrangian method for moving interfaces

A fast modular numerical method for solving general moving interface proble ms is presented. It simplifies code development by providing a black-box so lver which moves a given interface one step with given normal velocity. The method combines, an efficiently redistanced level set approach, a problem- independent velocity extension, and a second-order semi-Lagrangian time ste pping scheme which reduces numerical error by exact evaluation of the signe d distance function. Adaptive quadtree meshes are used to concentrate compu tational effort on the interface, so the method moves an N-element interfac e in O (N log N) work per time step. Efficiency is increased by taking larg e time steps even for parabolic curvature flows. Numerical results show tha t the method computes accurate viscosity solutions to a wide variety of dif ficult geometric moving interface problems involving merging, anisotropy, f aceting, nonlocality, and curvature. (C) 2000 Academic Press.