报告题目：An Energy-stable finite element method for nonlinear Maxwell equations

主讲人：吕茂辉

单位：中国科学院数学与系统科学研究院

时间：5月20日14:00-16:00

腾讯ID：224-902-489

密码：434828

摘要：In this talk, we consider the three-dimensional (3D) nonlinear Maxwell’s equations in the optical media characterized by linear Lorentz dispersion, nonlinear Kerr effect and delayed Raman scattering. Using Crank-Nicolson time discretization and special treatment of the nonlinearity, we propose a second order accurate (in time) finite element method for the nonlinear problem. Fully discrete energy stability analysis is established to show that the scheme is unconditionally stable. The nonlinear system is solved by Newton Krylov method. In order to efficiently solve the linearized algebraic system in each Newton sub-iteration, we further develop an effective preconditioner by using suitable approximations to the nonlinearity and the auxiliary space preconditioning technique. Numerical experiments are provided to examine the accuracy, the energy stability, the parallel scalability and the robustness in preconditioning of our proposed scheme. We then apply the scheme to simulate the spatial soliton propagation in 3D nonlinear glass. We also demonstrate the performance of the scheme in handling complex geometry through simulating the wave scattering by a spherical hole in the nonlinear optical glass.

简介：吕茂辉博士2013年本科毕业于重庆大学信息与计算科学专业。2020年获得重庆大学计算数学理学博士学位。2018年-2019年受国家留学基金委资助访问美国伦斯勒理工学院数学科学系。2020年至今在中国科学院数学与系统科学研究院计算数学与科学工程计算研究所从事博士后工作。博士后期间获得并主持中国博士后科学基金特别资助（站前）项目和国家自然科学基金青年基金项目。研究方向包括电磁波传播问题的高阶间断伽辽金方法和有限元方法、界面问题的高阶数值方法等。主要成果发表于Journal of Computational Physics和Journal of Scientific Computing等期刊上。