题目:Why spectral methods are preferred in PDE eigenvalue computations — in some cases?
报告人:张智民 教授 (北京计算科学研究中心)
邀请人:沈晓芹 教授(beat365官方最新版数学系)
报告时间:2022年6月16日上午10:00-12:00
线上会议:腾讯会议 ID:976-485-035
摘要: When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that spectral methods can outperform traditional methods and the state-of-the-art method in 2-D problems even with singularities.
报告人简介:张智民,美国韦恩州立大学教授、Charles H. Gershenson杰出学者,北京计算科学研究中心应用与计算数学研究部讲座教授,世界华人数学家大会45分钟报告人。2010年入选教育部高层次人才。曾任和现任Mathematics of Computation、Journal of Scientific Computing、Numerical methods for Partial Differential Equations、Journal of Computational Mathematics等多个国际计算数学杂志编委。张智民教授长期从事计算方法,尤其是有限元方法的研究,在超收敛、后验误差估计和自适应算法等领域取得了多项创新成果。首次提出了基于多项式守恒的离散重构格式,所提出的多项式保持重构(Polynomial Preserving Recovery—PPR)方法被国际上广为流行的大型商业软件COMSOL Multiphysics采用,发表SCI学术论文200余篇。