报告人：李猛 副教授 郑州大学
报告题目：On the rotating nonlinear Klein-Gordon equation with multiscale effects: structure-preserving methods and applications to vortex dynamics
摘 要：In this report, we study numerical methods for the rotating nonlinear Klein–Gordon (RKG) equation, a fundamental partial differential equation in relativistic quantum physics. The RKG equation models rotating galaxies under the Minkowski metric and also provides an effective description for phenomena such as cosmic superfluids. This work focuses on the development and rigorous analysis of structure-preserving Galerkin finite element methods (FEMs) for the RKG equation. A central challenge is that rotational terms prevent traditional nonconforming FEMs from simultaneously conserving energy and charge. By employing a conservation-adjusting technique, we have successfully constructed a consistent structure-preserving algorithm applicable to both conforming and nonconforming FEMs. Moreover, we provide a comprehensive convergence analysis, establishing the unconditional optimality and high-order accuracy of the proposed methods. These theoretical results are further validated through extensive numerical experiments, which demonstrate the accuracy, efficiency, and robustness of the structure-preserving schemes. Finally, simulations of vortex dynamics, spanning the relativistic to the nonrelativistic regime, are presented to illustrate vortex creation, relativistic effects on bound states, and the interaction of vortex pairs.
报告人简介：李猛，郑州大学副教授，毕业于华中科技大学数学与统计学院，新加坡国立大学访问学者。目前担任中国计算物理学会理事，仿真算法专委会委员。主要研究方向为曲率流、量子力学模型的保结构算法，相关工作发表在SIAM Journal on Multiscale Modeling and Simulation、IMA Journal of Numerical Analysis、Computer Methods in Applied Mechanics and Engineering、Journal of Nonlinear Science、Journal of Computational Physics、ESAIM: Mathematical Modelling and Numerical Analysis、Physica D、Computer Physics Communications等重要学术期刊上。2021年获得河南省自然科学奖二等奖。
报告时间：2026年5月29日，15:30--17:30
报告地点：数学科学学院512会议室
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内蒙古大学数学科学学院
2026年5月26日
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