报告题目：An Adaptive Finite Element DtN Method for Maxwell's Equations in Biperiodic Structures
报 告 人：吕俊良
工作单位：吉林大学
报告时间：2021-1-23 9:30-12:00；
腾讯会议ID：931 309 229
报告摘要：
Inthis talk，we consider the diffraction of an electromagnetic plane wave by a biperiodic structure where the wave propagation is governed by the three-dimensional Maxwell equations. Based on transparent boundary condition, the grating problem is formulated into a boundary value problem in a bounded domain. Using a duality argument technique, we derive an a posteriori error estimate for the finite element method with the truncation of the nonlocal Dirichlet-to-Neumann (DtN) boundary operator. The a posteriori error consists of both the finite element approximation error and the truncation error of boundary operator which decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is developed with error controlled by the a posterior error estimate, which determines the truncation parameter through the truncation error and adjusts the mesh through the finite element approximation error. Numerical experiments are presented to demonstrate the competitive behavior of the proposed adaptive method.
报告人简介：
吕俊良，吉林大学数学学院教授、博导。2009年博士毕业于吉林大学数学学院,导师李永海教授。2011-2013年于浙江大学做博士后研究，合作导师包刚教授。2015-2016年美国普渡大学访问学者，合作导师李培军教授。研究兴趣包括散射问题的自适应有限元方法及其理论分析，反散射问题的数值算法，辐射热传导问题的数值方法，有限体积元法的基础理论等。研究成果发表在SIAM J. Numer. Anal.，Math. Comput.及J.Sci. Comput.等杂志上。承担国家自然科学基金2项、国防科工局项目2项。
