At the invitation of the School of Mathematical Sciences, Nanjing Normal University, Professor Kei Fong Lam from Hong Kong Baptist University delivered an academic report entitled "A Phase Field Model for Stereolithography in 3D Printing: Analysis and Numerical Simulations" on June 9, 2026, at 2:30 PM in Room 526 of Xingjian Building. Faculty and students from the School of Mathematical Sciences attended the report.In his report, Professor Lam first introduced the development history and existing problems of stereolithography technology. In stereolithography, ultraviolet lasers cure photosensitive resin layer by layer, gradually transforming it from a liquid sol into a solid gel. This process involves multiple coupled physical mechanisms, including laser irradiation, polymerization, heat propagation, and the accumulation of mechanical properties. Professor Lam then introduced a phase field model to describe the sol-gel transition process. The phase field variable contains the resin conversion rate, while the temperature equation considers the heat generated by photopolymerization and laser absorption. The mechanical response is described by an elastic model, where the cured material has stiffness, while the uncured phase is considered a very soft elastic material. This avoids degradation, making the coupled partial differential equation systemboth analytically and computationally tractable. Together with his collaborators, Professor Kei Fong Lam constructed and analyzed an efficient fully discrete numerical scheme. This method employs piecewise linear finite elements in space and first-order discretization in time. To efficiently handle nonlinear double-well potentials, a scalar auxiliary variable method is used. This yields a linear implicit, unconditionally stable scheme that requires solving only the linear system at each time step. The analysis results include the existence and uniqueness of weak solutions, the convergence of the fully discrete approximation, and the optimal error estimate for the Caginalp subsystem. Finally, Professor Kei Fong Lam presented relevant numerical simulation results. In particular, this numerical method achieves second-order spatial accuracy under the L2 norm and first-order accuracy under the H1 norm, consistent with theoretical predictions.Following the report, faculty and graduate students from our institute engaged in an in-depth and enthusiastic discussion with Professor Kei Fong Lam, covering topics such as the application of discrete methods in other phase-field models and the extension of weak solution theory.Prof. Andrew Kei Fong Lam is an Associate Professor for the Department of Mathematics at Hong Kong Baptist University (HKBU). He earned his PhD at University of Warwick in 2014, followed by a postdoc in University of Regensburg, Germany, and returned to Hong Kong as a
Research assistant professor at the Chinese University of Hong Kong, before his tenure at Hong Kong Baptist University. His expertise lies in analysis of partial differential equations, specifically phase field models involving Cahn-Hilliard systems to describe multiphase dynamics, optimalcontrol with PDE constraints, and numerical analysis of structure prerserving schemes for simulations of multiphase dynamics.