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.
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.