High-order structure-preserving parametric finite element methods for geometric flows
报告专家：苏春梅 助理教授 清华大学
报告时间：7月24日（星期四），下午3:00-4:00
报告地点：数学学院西303
报告摘要：
Mesh quality is very essential for the simulation of geometric flows. Standard treatment may fail to work due to mesh distortion. In this talk, we propose a series of temporal high-order parametric finite element methods based on the BGN formulation for solving different types of geometric flows of curves and surfaces. Extensive numerical experiments demonstrate the expected high-order accuracy while maintaining favorable mesh quality throughout the evolution. Particularly, for those flows with multiple geometric structures, e.g., surface diffusion which decreases the area and preserves the volume, we propose a type of structure-preserving methods by incorporating two scalar Lagrange multipliers and two evolution equations involving the area and volume, respectively. These schemes can effectively preserve the structure at a fully discrete level. Extensive numerical experiments demonstrate that our methods achieve the desired temporal accuracy, as measured by the manifold distance, while simultaneously preserving the geometric structure of the surface diffusion.
专家简介：
2015年博士毕业于北京大学，此后先后在北京计算科学研究中心、新加坡国立大学、因斯布鲁克大学、慕尼黑工业大学做博士后研究。2021年被聘为清华大学丘成桐数学科学中心助理教授，研究方向为偏微分方程数值解。近年来主要研究几何偏分方程及色散类方程的计算方法及其分析。目前已在国际重要期刊如S1AM Journal on Numerical Analysis、SlAM Journal on Scientific Computing、Multiscale Modeling & Simulation、Numerische Mathematik、Mathematics of Computation、Foundations of Computational Mathematics、Journal of Computational Physics等发表论文三十余篇。
邀请人：唐庆粦
