Semi-implicit ADI operator-splitting method with Richardson extrapolation for the phase-field model of curvature-dependent tissue growth on surfaces

Authors: Zecheng Qiu, Yutong Wu, Yibao Li, Junxiang Yang

This paper presents a novel numerical framework for modeling curvature-dependent tissue growth on complex scaffolds. It is currently Under Review at Journal of Computational Physics (JCP).

Main Contributions:

• Developed and open-sourced a C++ simulation framework implementing a stabilized semi-implicit ADI operator-splitting solver, addressing the stability constraints of traditional explicit time-stepping.
• Achieved second-order temporal accuracy, enabling reliable long-time simulations with improved accuracy–cost balance.
• Extended the baseline 2D formulation to 3D volumetric geometries and implemented the corresponding solver pipeline, supporting simulations in realistic porous/scaffold-like structures.

Recommended citation: Z. Qiu, Y. Wu, Y. Li, J. Yang, Semi-implicit ADI operator-splitting method with Richardson extrapolation for the phase-field model of curvature-dependent tissue growth on surfaces, Submitted to Journal of Computational Physics (Under Review).
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