A variational method for multiphase volume-preserving interface motions

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 setti...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 257; pp. 157 - 179
Main Authors Svadlenka, Karel, Ginder, Elliott, Omata, Seiro
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2014
Subjects
Constrained variational problem
Mean curvature flow
Multiphase
Thresholding method
Volume preservation
76T30
Multiphase
53C44
Thresholding method
Constrained variational problem
35K55
65D18
Mean curvature flow
Volume preservation
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.08.027