Relaxation schemes for curvature-dependent front propagation

Authors

S Jin
MA Katsoulakis, University of Massachusetts - AmherstFollow
ZP Xin

Publication Date

1999

Journal or Book Title

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Abstract

In this paper we study analytically and numerically a novel relaxation approximation for front evolution according to a curvature-dependent local law. In the Chapman-Enskog expansion, this relaxation approximation leads to the level-set equation for transport-dominated front propagation, which includes the mean curvature as the next-order term. This approach yields a new and possibly attractive way of calculating numerically the propagation of curvature-dependent fronts. Since the relaxation system is a symmetrizable, semilinear, and linearly convective hyperbolic system without singularities, the relaxation scheme captures the curvature-dependent front propagation without discretizing directly the complicated yet singular mean curvature term.

Comments

The published version is located at http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0312(199912)52:12%3C1587::AID-CPA4%3E3.0.CO;2-A/abstract

Pages

1587-1615

Volume

52

Issue

12

Recommended Citation

Jin, S; Katsoulakis, MA; and Xin, ZP, "Relaxation schemes for curvature-dependent front propagation" (1999). COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. 472.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/472