报告题目 (Title)：Highly efficient and energy stable Multi-step SAV approaches for phase field models (相场模型的高效能量稳定多步SAV方法)

报告人 (Speaker)：陈艳萍 教授（南京邮电大学）

报告时间 (Time)：2024年12月10日(周二) 14:00-15:30

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：李常品、蔡敏

主办部门：理学院数学系

报告摘要：Recently, the scalar auxiliary variable (SAV) approach and its extended SAV-based approaches have been widely used to simulate a series of phase field models. However, many SAV-based schemes are known for the stability of a ‘modified’ energy. In this paper, we construct a series of modified SAV approaches with unconditional energy dissipation law based on several improvements to the traditional SAV approach. Firstly, by introducing the three-step technique, we can reduce the number of constant coefficient linear equations that need to be solved at each time step, while retaining all of its other advantages. Secondly, the addition of energy-optimized technique and SAV/Lagrange multiplier technique can make the numerical schemes have the advantage of preserving the original energy dissipation. Thirdly, we use the first-order approximation of the energy balance equation in the GSAV approach, instead of discretizing the dynamic equation of the auxiliary variable, so that we can construct the high-order unconditional original energy stable numerical schemes. Finally, representative numerical examples show that the efficiency and accuracy of the proposed schemes are improved.