2012/04/27 by Karel Švadlenka, Svadlenka, Karel, Elliott Ginder +3
Computer Science · Engineering · Materials Science · #35K55 #53C44 #65D18 #76T30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1204.6128
openalex publication_date 2012/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.