A fast shape transformation using a phase-field model

We propose a numerical method for a fast shape transformation using a phase-field model. The governing equation is based on the modified Allen–Cahn (AC) equation. We numerically solve the equation by using the operator splitting technique. The alternating direction explicit (ADE) finite difference method is used to reduce the strict temporal step constraint when solving the diffusion term. Therefore, we can use a large temporal step size to simulate a fast shape transformation. The reaction term is solved by the separation of variables, and the fidelity term is solved using the semi-implicit scheme with a frozen coefficient. To demonstrate that the proposed method can simulate the fast shape transformation with simple or complex sources and targets, we perform several numerical experiments in the three-dimensional space. The computational experiments demonstrate that the shape transformation is fast and smooth.