Applied Mathematics Seminar——High order in time, BGN-based parametric finite element methods for solving geometric flows
报告人：蒋维（武汉大学）
时间：2024-05-16 14:00-15:00
地点：智华楼-盈不足-109
报告摘要:
Geometric flows have recently attracted lots of attention from scientific computing communities. One of the most popular schemes for solving geometric flows is the so-called BGN scheme, which was proposed by Barrett, Garcke, and Nurnberg (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. Recently, based on a novel approach, we have successfully proposed temporal high-order, BGN-based parametric finite element method for solving geometric flows of curves/surfaces. Furthermore, we point out that the shape metrics (i.e., manifold 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 high-order in time in terms of the shape metric, and much more efficient than the classical BGN schemes.
个人简介:
蒋维，武汉大学数学与统计学院教授、博士生导师。2005年本科毕业于北京师范大学，2010年在welcome欢迎光临威尼斯公司获得理学博士学位。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，研究成果大多发表在SINUM、SIAP、SISC、IMAJNA、Acta Materialia、Scripta Materialia、PRB、PRMaterials、JCP等计算数学与材料科学权威期刊上。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。
