American Institute of Mathematical Sciences

October  2015, 8(5): 969-988. doi: 10.3934/dcdss.2015.8.969

Multiphase volume-preserving interface motions via localized signed distance vector scheme

 1 Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan 2 Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan

Received  December 2013 Revised  August 2014 Published  July 2015

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.
Citation: Rhudaina Z. Mohammad, Karel Švadlenka. Multiphase volume-preserving interface motions via localized signed distance vector scheme. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 969-988. doi: 10.3934/dcdss.2015.8.969
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