Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 257, Issue -, Pages 157-179Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2013.08.027
Keywords
Mean curvature flow; Volume preservation; Multiphase; Thresholding method; Constrained variational problem
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Funding
- JSPS KAKENHI [22740102, 23340024, 24654020]
- Grants-in-Aid for Scientific Research [25800087, 22740102, 24654020, 23340024] Funding Source: KAKEN
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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. (C) 2013 Elsevier B.V. All rights reserved.
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