走向现代数学学术报告 - 邬吉明研究员（No. 747) 

题目：An interpolation-free cell-centered finite volume scheme for diffusion/convection-diffusion equations on arbitrary polygonal/polyhedral meshes 

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21日 10:00 

地点：东海岸校区 - D实209 

摘要：We present a novel cell-centered finite volume discretization of the heterogeneous and anisotropic diffusion/convection-diffusion problems on polygonal/polyhedral meshes. The unknowns of the resulting linear scheme are the values at the cell centers, and no auxiliary unknowns are involved. The usual star-shaped assumption on the mesh is abolished, and we only require that each mesh cell is simply-connected. The new scheme has a small stencil, a nine-point stencil on the structured quadrilateral meshes, and a five-point one on the rectangular meshes if the diffusion coefficient is a scalar function. More important is that the new scheme has the ability to deal with arbitrary discontinuities. Numerical experiments show that the new linear finite volume scheme is robust and efficient, and maintains optimal convergence rates for the solution and flux in most extreme cases on general polygonal/polyhedral 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。