Semi-Lagrangian Methods for Level Set Equations

A new numerical method for solving geometric moving interface problems is presented. The method combines a level set approach and a semi-Lagrangian time stepping scheme which is explicit yet unconditionally stable. The combination decouples each mesh point from the others and the time step from the CFL stability condition, permitting the construction of methods which are efficient, adaptive, and modular. Analysis of a linear one-dimensional model problem suggests a surprising convergence criterion which is supported by heuristic arguments and confirmed by an extensive collection of two-dimensional numerical results. The new method computes correct viscosity solutions to problems involving geometry, anisotropy, curvature, and complex topological events.

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