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arXiv · 1204.6128

A variational method for multiphase area-preserving interface motions

Karel Svadlenka·Elliott Ginder·Seiro Omata
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Abstract

We develop a numerical method for realizing mean curvature motion of interfaces separating multiple phases, whose areas are preserved throughout time. The foundation of the method is a thresholding algorithm of the Bence-Merriman-Osher type. The original algorithm is reformulated in a vector setting, which allows for a natural inclusion of constraints, even in the multiphase case. Moreover, a new method for overcoming the inaccuracy of thresholding methods on non-adaptive grids is designed, since this inaccuracy becomes especially prominent in area-preserving motions. Formal analysis of the method and numerical tests are presented.

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Karel Svadlenka, Elliott Ginder, Seiro Omata. 2012-04-27. A variational method for multiphase area-preserving interface motions. https://arxiv.org/abs/1204.6128

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