Energy-conserving method for Stochastic Maxwell Equations with Multiplicative Noise
Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；School of Mathematical Science, China University of Mining and Technology（中国矿业大学数学科学学院）；School of Mathematical Science, Huaiyin Normal University（淮阴师范学院数学科学学院）
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic conservation law), and the energy of system is a conservative quantity almost surely. We propose a stochastic multi-symplectic energy-conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time. Numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy. The mean square convergence result of the method in temporal direction is tested numerically, and numerical comparisons with finite difference method are also investigated.
Two operator splitting methods for three-dimensional stochastic Maxwell equations with multiplicative noise
China University of Mining and Technology（中国矿业大学）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Shanghai Zhangjiang Institute of Mathematics（上海张江数学研究院）
Explicit charge-conserving and modified energy-conserving PIC methods using the SAV approach
University of Washington（华盛顿大学）；Inria Rennes (Mingus team) & IRMAR, UMR CNRS 6625, Univ Rennes（法国国家信息与自动化研究所雷恩分中心（Mingus团队）& IRMAR，CNRS联合研究单位6625，雷恩大学）
Mathematical and numerical analysis of the time-dependent Maxwell--Schrödinger Equations in the Coulomb gauge
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（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）；Department of Applied Mathematics, The Hong Kong Polytechnic University（香港理工大学应用数学系）
Mean-square convergence of a semi-discrete scheme for stochastic nonlinear Maxwell equations
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Applied Physics and Computational Mathematics（应用物理与计算力学研究所）
A Unified Hamiltonian Solution to Maxwell-Schrodinger Equations for Modeling Electromagnetic Field-Particle Interaction
University of Electronic Science and Technology of China（电子科技大学）；The University of Hong Kong（香港大学）；Fudan University（复旦大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
