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The segment projection method for interface tracking
Author(s) -
Tornberg AnnaKarin,
Engquist Björn
Publication year - 2003
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.10052
Subject(s) - discretization , mathematics , projection (relational algebra) , eulerian path , partial differential equation , interpolation (computer graphics) , level set method , grid , level set (data structures) , wavefront , tracking (education) , algorithm , computer science , geometry , computer vision , artificial intelligence , mathematical analysis , segmentation , motion (physics) , image segmentation , psychology , pedagogy , physics , lagrangian , optics
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. © 2002 Wiley Periodicals, Inc.