highly efficient and energy stable multi-step sav approaches for phase field models
报告人简介
陈艳萍，南京邮电大学博士生导师、国务院政府特殊津贴专家、教育部新世纪人才。中国工业与应用数学学会油水资源数值方法专业委员会副主任、国际数学建模挑战赛专家委员会和学术及顾问委员、 国际 sci 学术期刊《aamm》编委。主持获得教育部自然科学二等奖和广东省科学技术二等奖、参与获得国家教学成果二等奖和教育部自然科学一等奖等等。2014-2023 年连续 10 年入选 elsevier 中国高被引学者榜单，入选 2023 全球顶尖前 10 万科学家排名和数学类全球前 2%顶尖科学家榜单。主持国家自然科学基金重点项目 1 项和面上项目 8 项。
内容简介
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.
