A novel phase-field model for three-dimensional shape transformation

Abstract

We present a simple and robust numerical technique for a novel phase-field model of three-dimensional (3D) shape transformation. Shape transformation has been achieved using phase-field models. However, previous phase-field models have intrinsic drawbacks, such as shrinkage due to motion by mean curvature and unwanted growth. To overcome these drawbacks associated with previous models, we propose a novel phase-field model that eliminates these shortcomings. The proposed phase-field model is based on the Allen–Cahn (AC) equation with nonstandard mobility and a nonlinear source term. To numerically and efficiently solve the proposed phase-field equation, we adopt an operator splitting method, which consists of the AC equation with a nonstandard mobility and a fidelity equation. The modified AC equation is solved using a fully explicit finite difference method with a time step that ensures stability. For solving the fidelity equation, we use a semi-implicit scheme with a frozen coefficient. We have performed several numerical experiments with various 3D sources and target shapes to verify the robustness and efficacy of our proposed mathematical model and its numerical method.