Our latest work Two lower boundedness-preservity auxiliary variable methods for a phase-field model of 3D narrow volume reconstruction has been published to CNSNS recently.

By employing scattered point data, our approach reconstructs smooth narrow volumes using a phase-field Allen–Cahn model with a control function. The proposed method ensures energy dissipation and smooth surface throughout the reconstruction process. By introducing an auxiliary variable, the nonlinear term in the governing equation is reformulated, allowing for efficient time-marching schemes. The fully discrete scheme is linear, and its unconditional stability is rigorously estimated.

If you are interested in our work, please kindly follow the link below:
https://www.sciencedirect.com/science/article/abs/pii/S1007570425000607