A variational method for multiphase volume-preserving interface motions

Authors:
Karel Svadlenka;Elliott Ginder;Seiro Omata
Affiliations:
-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

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Abstract

We develop a numerical method for realizing mean curvature motion of interfaces separating multiple phases, whose volumes 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 volume-preserving motions. Formal analysis of the method and numerical tests are presented.