讲座主题：Anisotropic adaptive moving meshes for 3D singularly perturbed reaction-diffusion problems

专家姓名：刘利斌

工作单位：南宁师范大学

讲座时间：2026年11月13日 15:00-16:00

讲座地点：腾讯会议：486-944-945

主办单位：烟台大学数学与信息科学学院

内容摘要：

A class of three-dimensional singularly perturbed steady semilinear reactiondiffusion problems is considered. A pseudo-time formulation is introduced for the steady problem, and an alternating direction implicit (ADI) finite difference method is employed, reducing each pseudo-time correction to a sequence of one-dimensional tridiagonal solves. A maximum-norm a posteriori error estimate is used to construct directional monitor functions for mesh redistribution. The resulting moving-mesh algorithm consists of three decoupled one-dimensional equidistribution procedures along the coordinate directions, and thus generates solution-adaptive anisotropic tensor-product meshes without prescribed transition points. The linewise independence induced by the ADI factorization is exploited in a HIP-based GPU implementation, where the directional families of tridiagonal systems are processed concurrently, together with parallel residual evaluation, monitor construction, and norm reduction. Numerical experiments demonstrate that boundary, edge, and corner layers are effectively resolved, and robust second-order convergence is maintained uniformly with respect to the diffusion coefficient.

主讲人介绍：

刘利斌，博士，教授，硕士生导师，广西第二批高等学校千名骨干教师。主持完成国家自然科学基金天元访问学者项目，青年基金和地区基金各一项；主持完成广西区自然科学基金项目青年项目和面上项目各一项。主要研究兴趣为奇异摄动问题的自适应网格算法、分数阶微分方程数值解法和智能算法及其应用。在Journal of Science and Computing, Numerical Algorithms, Journal of Computational and Applied Mathematics等期刊上发表学术论文30多篇。