An improvement of level set equations via approximation of a distance function

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.

KEYWORDS:

• Level set method
• improved level set equations
• signed distance function
• viscosity solutions

AMS SUBJECT CLASSIFICATIONS:

• 35D40
• 35F21
• 35F25

Acknowledgements

The author is grateful to Professor Norikazu Yamaguchi for discussions on numerical computations and permission to use the figures in this paper. The author also thanks the anonymous referees for his/her careful reading of the manuscript and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Young Scientists (B) No. 16K17621.