In this paper we establish the convergence of three computational algorithms for interface motion in a multi-phase system, which incorporate bulk effects. The algorithms considered fall under the classification of thresholding schemes, in the spirit of the celebrated Merriman–Bence–Osher algorithm for producing an interface moving by mean curvature. The schemes considered here all incorporate either a local force coming from an energy in the bulk, or a non-local force coming from a volume constraint. We first establish the convergence of a scheme proposed by Ruuth-Wetton for approximating volume-preserving mean-curvature flow. Next we study a scheme for the geometric flow generated by surface tension plus bulk energy. Here the limit is motion by mean curvature (MMC) plus forcing term. Last we consider a thresholding scheme for simulating grain growth in a polycrystal surrounded by air, which incorporates boundary effects on the solid-vapor interface. The limiting flow is MMC on the inner grain boundaries, and volume-preserving MMC on the solid-vapor interface.
1
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leizpig, Germany
2
Purdue University, West Lafayette, USA
Tim Laux; Drew Swartz. Convergence of thresholding schemes incorporating bulk effects. Interfaces and free boundaries, Tome 19 (2017) no. 2, pp. 273-304. doi: 10.4171/ifb/383
@article{10_4171_ifb_383,
author = {Tim Laux and Drew Swartz},
title = {Convergence of thresholding schemes incorporating bulk effects},
journal = {Interfaces and free boundaries},
pages = {273--304},
year = {2017},
volume = {19},
number = {2},
doi = {10.4171/ifb/383},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/383/}
}
TY - JOUR
AU - Tim Laux
AU - Drew Swartz
TI - Convergence of thresholding schemes incorporating bulk effects
JO - Interfaces and free boundaries
PY - 2017
SP - 273
EP - 304
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/383/
DO - 10.4171/ifb/383
ID - 10_4171_ifb_383
ER -
