汇报标题 (Title)：An Efficient Spectral Method for Singularly Perturbed Convection-Diffusion-Reaction Problems in Three-Dimensional Irregular Exterior Domains（三维不规定表域奇扰动对流扩散反映问题的高效谱法)
汇报人 (Speaker)：王中庆 教授（上海理工大学）
汇报功夫 (Time)：2025年11月13日（周四）9:00
汇报地址 (Place)：腾讯会议 938-559-552
约请人(Inviter)：朱佩成
主办部门：理学院数学系
汇报提要：
This paper presents an efficient Fourier - Legendre - Jacobi rational spectral method , based on mapping techniques , for solving singularly perturbed convection - diffusion - reaction problems in a three - dimensional exterior domain with a complex obstacle . The solutions exhibit bound - ary or interior layer behavior as e →0. The method begins by applying a spherical coordinate transformation to map the exterior domain of the complex obstacle onto the exterior of a unit sphere , while simultaneously transforming the convection - diffusion - reaction equation . The transformed equation is then formulated in its weak form , and a Fourier - Legendre - Jacobi rational spectral scheme is introduced . The paper provides a detailed description of the numerical implementation and analyzes the convergence of the solution in the H - norm . Numerical results demonstrate that the proposed method achieves high - order accuracy .
