报告题目：量子计算中的高阶守恒型数值方法
报告人：李祥贵 教授（北京信息科技大学）
时间：2020年9月22日上午10:00-11:00
方式：腾讯会议 ID: 944 370 060
主持人：王廷春 教授
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. Then extending the high-order operator-compensation methods can also be shown to keep mass and energy conservation. Some numerical results for BEC are given.
报告人简介：李祥贵，现为北京信息科技大学理学院教授，校外兼职博士生导师。曾多次到新加坡、香港、澳大利亚，巴西等地的大学和研究机构开展学术交流与科研合作。已发表论文60余篇，其中被SCI、EI收录50余篇；三次获省部级教学、科研成果奖；专利授权2项，出版专著2本 ；主持完成国家自然科学基金3项，国防基础科研科学挑战计划等项目10余项。曾任北京信息科技大学党委研工部部长、理学院院长。现为全国计算数学学会理事、北京计算数学学会理事。
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数学与统计学院
2020年9月18日