报告承办单位: 数学与统计学院

报告题目: A unified energy-dissipative framework for non-isothermal anisotropic dendritic growth via enthalpy reformulation

报告人姓名: 张弘

报告人所在单位: 国防科技大学

报告人职称/职务及学术头衔: 副教授

报告时间: 2026年6月11日下午 16:30-18:30

报告地点: 云塘校区理科楼A212

邀请人: 刘乐乐

报告摘要:A canonical model for describing anisotropic dendritic growth is the non-isothermal gradient flow system, which couples an Allen-Cahn phase-field equation with the evolution of temperature. This coupled system presents severe challenges for efficient numerical discretization: double time derivatives in the temperature equation, strong stiffness and nonlinearity induced by anisotropic interfacial energy, the double-well potential, and latent heat coupling, as well as the inherent difficulty of preserving the original energy dissipation law. To address these, we develop a unified energy-dissipative framework for both exponential-time-differencing Runge-Kutta and implicit-explicit Runge-Kutta integrators. The novelty lies in a structure-preserving enthalpy reformulation that eliminates time-derivative coupling and recovers a hidden mixed $L^2$-$H^{-1}$ variational structure, paired with a sharp double stabilization strategy enabling explicit discretization of nonlinearities. Using a matrix-vector formulation, we rigorously prove the unconditional energy dissipation of proposed schemes, with numerical experiments verifying up-to-fourth-order convergence and robust performance for dendritic growth simulation.

报告人简介: 张弘，国防科技大学理学院数学系副教授，硕士生导师。2012年毕业于浙江大学数学系，2014年获国防科学技术大学硕士学位，2018年获荷兰乌特勒支大学数学博士学位。主要从事偏微分方程保结构算法、自适应方法的研究。在SIAM Numer. Anal., SIAM J. Sci. Comput., J. Comput. Phys.等期刊发表论文60余篇，入选湖南省青年A类项目，荷尖人才，国防科技大学高层次创新人才。主持国家自然科学基金面上、青年项目、军委科技委项目等。