Abstract
We review some of the motivation and development of the Voronoi Implicit Interfaces Method (VIIM), first introduced in [10], for tracking multiple interacting and evolving regions, whose motion is determined by complex physics that include hydrodynamic, elastic, and geometric forces. The method automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions, and topological changes in the system occur naturally, with no surgery required.
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This work was supported in part by the Applied Mathematical Science subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract Number DE-AC02-05CH11231, by the Computational Mathematics Program of the National Science Foundation, and by NCI U54CA143833. Some computations used the resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. J.S. was also supported by the Miller Foundation at UC Berkeley, and as an Einstein Visiting Fellow of the Einstein Foundation, Berlin. R.S. was also supported by an American Australian Association Sir Keith Murdoch Fellowship.
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Saye, R.I., Sethian, J.A. The Voronoi Implicit Interface Method and Computational Challenges in Multiphase Physics. Milan J. Math. 80, 369–379 (2012). https://doi.org/10.1007/s00032-012-0187-6
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DOI: https://doi.org/10.1007/s00032-012-0187-6