An improvement of level set equations via approximation of a distance function. Issue 10 (27th July 2019)

• Record Type: Journal Article
• Authors: Hamamuki, Nao
• Is Part Of: Applicable analysis. Volume 98:Issue 10(2019)
• Page Start: 1901
• Page End: 1915
• Publication Date: 2019-07-27
• Subjects: Level set method -- improved level set equations -- signed distance function -- viscosity solutions; 35D40 -- 35F21 -- 35F25; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1484911
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In the classical level set method, the slope of solutions can be very small or large, and it can make it difficult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper- and lower bound near the zero level set for the viscosity solution to the initial value problem.