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Mathematics Group

Level Set Methods for Propagating Interfaces

Level set methods are computational methods for tracking moving interfaces. They rely on a central embedding of a moving front as the zero level set of an implicitly defined function, which results in an initial value Hamilton-Jacobi equation, and is accurately and efficiently solved by building on numerical schemes originally designed for hyperbolic conservation laws. They handle topological change, sharp corners and cusps, and naturally lend themselves to computational problems in which geometry, complex physics, and intricate jump conditions are deeply intertwined. They are widespread throughout computational physics, and are used to compute two-phase flow in such areas as mixing devices, etching and deposition in semiconductor manufacturing, crack and fracture dynamics in material failure, and ground water transport.