Special Session 83: New Aspects of Mathematical Modeling and Analysis in Materials Science

A threshold-type algorithm for fourth order geometric motions
Katsuyuki Ishii
Kobe University
Japan
Co-Author(s):    
Abstract:
In this talk, we are concerned with a numerical algorithm for the motion of hypersurfaces/curves by the fourth order geometric equations such as the Willmore flow equation. The algorithm we introduce here was first proposed by Bence, Merriman and Osher in 1991 to numerically compute mean curvature flows. Our algorithm is an application of theirs and we use the fourth order heat equation instead of the second order one. We present the asymptotic expansion of the solution for the fourth order heat equation and the consistency result. This talk is based on my joint work with Professors Y. Kohsaka (Kobe U.), N. Miyake (Kyushu U.) and K. Sakakibara (Kanazawa U. \& RIKEN).