Level Set Methods And Dynamic Implicit Surfaces by Stanley J. Osher

A compact introduction to the mathematical foundations and numerical techniques for representing and evolving interfaces implicitly as the zero level set of a higher-dimensional function; it presents the governing PDEs (Hamilton–Jacobi type and curvature-driven flows), the viscosity-solution framework, and stable high-resolution discretizations (upwind, ENO/WENO, reinitialization) while demonstrating applications in multiphase fluid dynamics, image processing, shape optimization and related problems, with emphasis on robustness for topological changes and accurate computation of geometric quantities.

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