Level Set Equations on Surfaces via the Closest Point Method

Abstract Level set methods have been used in a great number of applications in R2 and R3 and it is natural to consider extending some of these methods to problems defined on surfaces embedded in R3 or higher dimensions. In this paper we consider the treatment of level set equations on surfaces via a recent technique for solving partial differential equations (PDEs) on surfaces, the Closest Point Method [18]. Our main modification is to introduce a Weighted Essentially Non-Oscillatory (WENO) interpolation step into the Closest Point Method. This, in combination with standard WENO for Hamilton

• Type: Journal
• Year: 2008
• Where: JSCIC
• Authors: Colin B. Macdonald, Steven J. Ruuth
• Keywords: Closest Point Method, JSCIC 2008, Smooth Test Problems, Surfaces