A conservative local discontinuous Galerkin method for the solution of nonlinear Schrdinger equation in two dimensions  

作　　者：ZHANG RongPei YU XiJun LI MingJun LI XiangGui 

机构地区：[1]School of Mathematics and Systematic Sciences, Shenyang Normal University [2]Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics [3]School of Mathematics and Computational Science, Xiangtan University [4]School of Applied Science, Beijing Information Science and Technology University

出　　处：《Science China Mathematics》2017年第12期2515-2530,共16页中国科学：数学（英文版）

基　　金：supported by the Foundation of Liaoning Educational Committee (Grant No. L201604);China Scholarship Council, National Natural Science Foundation of China (Grant Nos. 11571002, 11171281 and 11671044);the Science Foundation of China Academy of Engineering Physics (Grant No. 2015B0101021);the Defense Industrial Technology Development Program (Grant No. B1520133015)

摘　　要：In this study, we present a conservative local discontinuous Galerkin(LDG) method for numerically solving the two-dimensional nonlinear Schrdinger(NLS) equation. The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux. The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central, alternative and upwind-based flux. We will propose two kinds of time discretization methods for the semi-discrete formulation. One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation. The other one is Krylov implicit integration factor(IIF) method which demands much less computational effort. Various numerical experiments are presented to demonstrate the conservation law of mass and energy, the optimal rates of convergence, and the blow-up phenomenon.In this study, we present a conservative local discontinuous Galerkin（LDG） method for numerically solving the two-dimensional nonlinear Schrdinger（NLS） equation. The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux. The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central, alternative and upwind-based flux. We will propose two kinds of time discretization methods for the semi-discrete formulation. One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation. The other one is Krylov implicit integration factor（IIF） method which demands much less computational effort. Various numerical experiments are presented to demonstrate the conservation law of mass and energy, the optimal rates of convergence, and the blow-up phenomenon.

关 键 词：discontinuous Galerkin method nonlinear Schrdinger equation CONSERVATION Krylov implicit integration factor method 

分 类 号：O241.82[理学—计算数学]