汇报标题 (Title)：Energy-Dissipative Spectral Renormalization Exponential Integrator Method for Gradient Flow Problems (梯度流问题的能量耗散谱沉整指数积分步骤)
汇报人 (Speaker)：鞠立力 教授（美国南卡罗莱纳大学）
汇报功夫 (Time)：2023年11月30日(周四) 10:00
汇报地址 (Place)：腾讯会议(349-118-102)
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：In this talk, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and achieve high-order accuracy in time. To accomplish this, our method first incorporates the energy dissipation law into the target gradient flow equation by introducing a time-dependent spectral renormalization (TDSR) factor. Then, the coupled equations are discretized using the spectral approximation in space and the exponential time differencing (ETD) in time. Finally, the resulting fully discrete nonlinear system is decoupled and solved using the Picard iteration at each time step. Furthermore, we introduce an extra enforcing term into the system for updating the TDSR factor, which greatly relaxes the time step size restriction of the proposed method and enhances its computational efficiency. Extensive numerical tests with various gradient flows are presented to demonstrate the accuracy and effectiveness of our method as well as its high efficiency when combined with an adaptive time-stepping strategy for long-term simulations.
