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 algo rithms and extracting the moving interface with a fast new contouring techn ique. 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, compu tes highly accurate solutions to geometric moving-interface problems involv ing merging, anisotropy, and faceting; with a high-order embedded geometry module, it solves second-order problems involving curvature, dynamic topolo gy, and nonlocal interactions. (C) 2001 Academic Press.