MULTIPHASE VOLUME-PRESERVING INTERFACE MOTIONS VIA LOCALIZED SIGNED DISTANCE VECTOR SCHEME

作者：Mohammad Rhudaina Z^*; Svadlenka Karel

来源：Discrete and Continuous Dynamical Systems - Series S, 2015, 8(5): 969-988.

DOI：10.3934/dcdss.2015.8.969

• Multiphase mean curvature flow
• vector-valued signed distance
• volume preservation
• constrained variational method
• BMO thresholding

We develop a signed distance vector approach for approximating volume-preserving mean curvature motions of interfaces separating multiple phases a variant of the BMO (Bence-Merriman-Osher) thresholding dynamics. We adopt a variational method employing the idea of a vector-type discrete Morse flow, which allows us to easily treat volume constraint via penalization without having to change the threshold value. Moreover, employing a vector-valued analogue of the signed distance function, the scheme is designed to allow subgrid accuracy on uniform grids without adaptive refinement; thereby, alleviating the well-known BMO time and grid restrictions. Finally, we present numerical tests and examples.

• 出版日期2015-10