报告题目：A Second-order in time, BGN-based parametric finite element method for geometric flows of curves

报告时间：2023年7月19日（星期三）上午10:30-11:30

报告地点：藕舫楼629会议室

报告人：蒋维 副教授

主持人：王廷春 教授

报告摘要：Geometric flows have recently attracted lots of attention from scientific computing communities. One of the most efficient numerical schemes for solving geometric flows is the well-known BGN scheme, which was proposed by Barrett, Garcke, and N\urnberg (J. Comput. Phys., 222 (2007), pp.~441--467). However, the BGN scheme only can attain first-order accuracy in time, and how to design a temporal high-order numerical scheme is challenging. In this paper, we propose a temporal second-order, BGN-based parametric finite element method for solving geometric flows of curves. The key idea lies in that the chosen discrete inner product over the curve $\Gamma^m$ at which the time is exactly the same as the time when all quantities are the approximations with an error of $\mathcal{O}(\tau^2)$, where $\tau$ is the time step size. Furthermore, we point out that the shape metrics (i.e., manifold distance and Hausdorff distance), instead of the function norms, should be used to measure numerical errors of the proposed schemes. Finally, ample numerical experiments demonstrate that the proposed BGN-based schemes are second-order in time in the sense of the shape metric, and much more efficient than the first-order BGN schemes. This is a joint work with Chunmei Su and Ganghui Zhang.

专家简介：蒋维，武汉大学JS金沙副教授、博士生导师。2005年本科毕业于北京师范大学，2010年在北京大学获得理学博士学位。现主要从事材料科学中的数学问题和几何偏微分方程数值算法的研究。目前，在数学和材料科学交叉研究课题上，以第一作者/通讯作者在SINUM、SIAP、SISC、IMAJNA、Acta Materialia、Scripta Materialia、PRB、PRMaterials、JCP等国际期刊上发表学术论文三十多篇。曾多次学术访问美国、欧洲、新加坡、香港等地的著名学术机构，主持国家自然科学基金面上项目两项，正参与国家重点研发计划项目一项,  参与完成国家自然科学基金重大研究计划集成项目一项。

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JS金沙

2023年7月17日