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The segment projection method for interface tracking. (English) Zbl 1205.76205

Summary: There has recently been important progress in the development of front tracking and level set methods for the numerical simulation of moving interfaces. The segment projection method is a new technique for computational geometry. It can be seen as a compromise between front tracking and level set methods. It is based on the regular mathematical representation of a manifold as an atlas of charts. Each chart or segment is evolved independently by a partial differential equation that is discretized on an Eulerian grid. The connectivity of the segments is handled by an appropriate data structure and by numerical interpolation. The method is presented and its properties are analyzed. Applications to multiphase flow, epitaxial growth, and high-frequency wave propagation are given.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
74N99 Phase transformations in solids
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