走向现代数学学术报告 - 邬吉明研究员（No. 748) 

题目：Vertex-centered linearity-preserving schemes for radiation diffusion problems on polygonal grids 

报告人：邬吉明 研究员（北京应用物理与计算数学研究所） 

时间：2024年11月22日 9:00 

地点：东海岸校区 - D实209 

摘要：We present two vertex-centered finite volume schemes for the numerical solution of radiation diffusion problems on arbitrary polygonal meshes. The first scheme is a linear one with unknowns defined at the cell vertices. It is locally conservative with respect to the dual mesh, captures exactly the piecewise linear solutions, leads to a symmetric positive definite matrix, and yields a nine-point stencil on structured quadrilateral meshes. The coercivity, stability and H1 error estimate of the scheme are obtained under some weak geometry assumptions. The second scheme is a nonlinear one that is linearity-preserving and positivity-preserving. Unlike most existing positivity-preserving finite volume schemes, the construction of the scheme is based on a novel nonlinear two-point flux approximation that has a fixed stencil and does not require the convex decomposition of the co-normal. Both schemes can be easily extended to the polyhedral meshes. Numerical experiments show that the two schemes are robust and efficient, and have optimal convergence rates for the solution and flux on general polygonal meshes. 

报告人简介：邬吉明，北京应用物理与计算数学研究所研究员，博士生导师。1999 年毕业于中国科学院计算数学与科学工程计算研 究所，获理学博士学位。1999 年7 月到北京应用物理与计算数学研究所做博士后，2001 年5 月出站后留所，长期负责 Z-pinch 数值模拟程序 MARED 的研制工作。研究兴趣涉及区域分解，超奇异积分计算，有限体积法等，近年来主要从事 辐射扩散方程有限体积方法方面的研究。在SIAM J.Sci. Comput.、Numer. Math.、J. Comput. Phys.、Methods Appl. Mech. Engrg.、IMA J. Numer. Anal.、J. Sci. Comput.，《计算数学》等国内外重要学术期刊上发表论文90多篇，其中 SCI期刊论文60多篇，所发表论文被SCI期刊他引700多次。曾主持国家自然科学基金项目4项，获军队科技进步二等奖1项。