Piecewise Constant Level Set Method for Multiphase Motion

Abstract

We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-splitting schemes are used to solve the problem efficiently. Numerical experiments are supplied to show the efficiency for motion by mean curvature for multiphase problems.