活動(dòng)主題：計(jì)算數(shù)學(xué)及其交叉學(xué)科前沿系列講座報(bào)告
報(bào)告題目：A coupled WG-MSE method for Schr?dinger eigenvalue problem with an inverse square potential
報(bào)告人：翟起龍 副教授 吉林大學(xué)
邀請人：董灝博士
報(bào)告時(shí)間：2024年9月27日(星期五)下午2:00-5:00
騰訊會(huì)議ID：245-744-483
報(bào)告人簡介：翟起龍，吉林大學(xué)副教授，主要從事特征值問題高精度數(shù)值方法領(lǐng)域的研究，特別是對求解偏微分方程特征值問題的非標(biāo)準(zhǔn)有限元方法以及深度學(xué)習(xí)方法進(jìn)行了深入探索，在計(jì)算數(shù)學(xué)高水平期刊發(fā)表SCI論文30余篇。翟起龍于2022年入選首屆中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)青年人才托舉工程項(xiàng)目，同年獲吉林省自然科學(xué)獎(jiǎng)一等獎(jiǎng)（第二完成人），主持國家自然科學(xué)基金面上項(xiàng)目、青年基金等項(xiàng)目。
報(bào)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 Schr?dinger 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.
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
