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

Rhudaina Z.  Mohammad; Karel Švadlenka

doi:10.3934/dcdss.2015.8.969

Article Contents

2015, Volume 8, Issue 5: 969-988. Doi: 10.3934/dcdss.2015.8.969

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

Rhudaina Z. Mohammad^1, and
Karel Švadlenka^2,

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

Received: December 2013

Revised: August 2014

Published: October 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 53C44, 76T30; Secondary: 35K55.

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