报告题目：Conservative High-Order Numerical Schemes for Quantum Computation
报 告 人：李祥贵，北京信息科技大学理学院，教授
报告时间：2019年12月11日下午 3:30-4:30
报告地点：阳明学院一楼报告厅
报告摘要：In this talk, based on the operator-compensation method, a semi-discrete scheme, which is of any even order accuracy in space, with charge and energy conservation is proposed to solve the nonlinear Dirac equation (NLDE) . Then this semi-discrete scheme can be discretized in time by the second-order accuracy time-midpoint (or Crank-Nicolson) method or the time-splitting method, we therefore obtain two kinds of full discretized numerical methods. For the scheme derived the time-midpoint method, it can be proved to conserve charge and energy in the discrete level, but the other one, it can only be proved to satisfy the charge conservation. These properties of the schemes with any even order accuracy are proved theoretically by a rigorous way in this paper. Some numerical experiments for 1D and/or 2D NLDE are given to test the accuracy order and verify the stability and conservation laws for our schemes. In addition, the binary and ternary collisions for 1D NLDE and the dynamics of 2D NLDE are also discussed. This numerical method can also be extended to solve the nonlinear Schrödinger equation.
专家简介：李祥贵，北京信息科技大学教授，曾任该校理学院院长，校研工部部长兼研究生院副院长，北京高校数学教育发展研究中心常务副主任，计算数学等学会理事，2002年在北京应用物理与计算数学研究所获博士学位，主要从事计算数学研究，已在Numer Math, JCP等国内外重要刊物发表论文数十篇。
