活动主题：计算数学及其交叉学科前沿系列讲座报告

报告题目：A coupled WG-MSE method for Schrödinger eigenvalue problem with an inverse square potential

报告人：翟起龙 副教授 吉林大学

邀请人：董灏博士

报告时间：2024年9月27日(星期五)下午2:00-5:00

腾讯会议ID：245-744-483

报告人简介：翟起龙，吉林大学副教授，主要从事特征值问题高精度数值方法领域的研究，特别是对求解偏微分方程特征值问题的非标准有限元方法以及深度学习方法进行了深入探索，在计算数学高水平期刊发表SCI论文30余篇。翟起龙于2022年入选首届中国工业与应用数学学会青年人才托举工程项目，同年获吉林省自然科学奖一等奖（第二完成人），主持国家自然科学基金面上项目、青年基金等项目。

报告摘要：In this talk, we introduce a weak Galerkin (WG) finite element method coupled with mortar spectral element method (MSEM) to solve the Schrödinger eigenvalue problem with an inverse square potential. For the domain around the inverse square potential, we use the mortar spectral element method to simulate the singularities in eigenfunctions caused by the inverse square potential, while we employ the WG method in the remaining domain. This coupled method can effectively handle the singularity arising from the inverse square potential. Notably, hanging nodes are allowed on the coupled interface. Compared to the conforming finite element method coupled with MSEM, our approach is not constrained by the mesh size of the mortar spectral element. This flexibility permits the use of fine meshes in the WG domain, thereby enhancing accuracy. We provide hp error analysis for both eigenfunctions and eigenvalues. Numerical experiments demonstrate the hp convergence of the theoretical results.

主办单位：数学与统计学院