Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 105–121
Abstract
Geometric partial differential equations of level-set form are usually constructed by a variational method using either Dirac delta function or co-area formula in the energy functional to be minimized. However, the equations derived by these two approaches are not consistent. In this paper, we present a third approach for constructing the level-set form equations. By representing various differential geometry quantities and differential geometry operators in terms of the implicit surface, we are able to reformulate three classes of parametric geometric partial differential equations (second-order, fourth-order and sixth-order) into the level-set forms. The reformulation of the equations is generic and simple, and the resulting equations are consistent with their parametric form counterparts. We further prove that the equations derived using co-area formula are also consistent with the parametric forms. However, these equations are of much more complicated forms than these given by the equations we derived.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.09-m2971
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 1 : pp. 105–121
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Geometric partial differential equations Level set Differential geometry operators.