A Fast Modular Semi-Lagrangian Method for Moving Interfaces

A fast modular numerical method for solving general moving interface problems is presented. It simplifies code development by providing a black-box solver 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 stepping scheme which reduces numerical error by exact evaluation of the signed distance function. Adaptive quadtree meshes are used to concentrate computational effort on the interface, so the method moves an N-element interface in O(N log N) work per time step. Efficiency is increased by taking large time steps even for parabolic curvature flows. Numerical results show that the method computes accurate viscosity solutions to a wide variety of difficult geometric moving interface problems involving merging, anisotropy, faceting, nonlocality, and curvature.