A Fast Semi-Lagrangian Contouring Method for Moving Interfaces

General moving-interface problems are solved by a new approach: evaluating an explicit semi-Lagrangian advection formula with efficient geometric algorithms and extracting the moving interface with a fast new contouring technique. The new approach decouples spatial and temporal resolutions, and grid-free adaptive refinement of the interface increases accuracy dramatically. A modular implementation, with a fast new intrinsic geometry module, computes highly accurate solutions to geometric moving-interface problems involving merging, anisotropy, and faceting; with a high-order embedded geometry module, it solves second-order problems involving curvature, dynamic topology, and nonlocal interactions.