Structure-preserving numerical scheme for a generalized area-preserving crystalline curvature flow

Structure-preserving numerical scheme for a generalized area-preserving crystalline curvature flow

Tetsuya Ishiwata1, Shigetoshi Yazaki2

1College of Systems Engineering and Science, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ka, Saitama 337-8570, Japan.

2School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kanagawa 214-8571, Japan.



The presented numerical scheme preserves variational structure of a generalized area-preserving crystalline curvature flow.   The scheme is based on an iteration and a projection method. Several numerical examples will verify that the enclosed area is preserved in numerical computation with high accuracy in the sense of double precision. Numerical computations realize theoretical convexification results starting from almost convex polygon, and are extended to a general setting starting from nonconvex polygon. 

Cite as:

Ishiwata, T., Yazaki, S. (2017). Structure-preserving numerical scheme for a generalized area-preserving crystalline curvature flow. Computer Methods in Materials Science, 17(2), 122 – 135.

Article (PDF):


Structure-preserving, Area-preserving crystalline curvature flow, Iteration, Convexification, Negative crystal, Accurate numerical compuatation


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