Calculus of Variations and Geometric Measure Theory
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P. Dondl - S. Wojtowytsch

Keeping it together: a phase field version of path-connectedness and its implementation

created by wojtowytsch on 13 Sep 2018

[BibTeX]

preprint

Inserted: 13 sep 2018

Year: 2018

ArXiv: 1806.04767 PDF

Abstract:

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are presented. First, a discrete steepest decent of a phase field version of a bending energy with spontaneous curvature and additional surface area penalty is shown, which leads to disconnected surfaces without our topological constraint but connected surfaces with the constraint. The second application is the segmentation of an image into a connected component and its exterior. Numerically, our constraint is treated using a suitable geodesic distance function which is computed using Dijkstra's algorithm.

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