Geodesic
Convergence of a threshold-type algorithm using the signed distance function
Katsuyuki Ishii1 orcid ; Masato Kimura2
1Kobe University, Japan
2Kanazawa University, Japan
Interfaces and free boundaries, Tome 18 (2016) no. 4, pp. 479-522

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DOI

We consider a threshold-type algorithm for curvature-dependent motions of hypersurfaces. This algorithm was numerically studied by [27], [9] and [35], where they used the signed distance function. It is also regarded as a variant of the Bence–Merriman–Osher algorithm for the mean curvature flow ( [4]). In this paper we prove the convergence of our algorithm under the nonfattening condition, applying the method of [30] which is based on the notion of the generalized flow due to [3]. Then we derive the rate of convergence of our algorithm to the smooth and compact curvature-dependent motions and show its optimality to the special case of a circle evolving by its curvature. We also give a local estimate on the convergence to a regular portion of the generalized curvature-dependent motion.
DOI : 10.4171/ifb/371
Classification : 35-XX, 65-XX
Mots-clés : Threshold-type algorithm, curvature-dependent motions, signed distance function

Katsuyuki Ishii  1   ; Masato Kimura  2

1 Kobe University, Japan
2 Kanazawa University, Japan 
Katsuyuki Ishii; Masato Kimura. Convergence of a threshold-type algorithm using the signed distance function. Interfaces and free boundaries, Tome 18 (2016) no. 4, pp. 479-522. doi: 10.4171/ifb/371
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     year = {2016},
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