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報告題目：量子計算中的高階守恒型數(shù)值方法

主講人：李祥貴教授 （北京信息科技大學(xué)）      

時間：2021年4月16日（周五）16:00 p.m.

形式：線上講座      

主辦單位：統(tǒng)計與數(shù)學(xué)學(xué)院

     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 Schr?dinger 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.

     主講人簡介：    

李祥貴，現(xiàn)任北京信息科技大學(xué)教授，北京高校數(shù)學(xué)教育發(fā)展研究中心常務(wù)副主任，中國計算數(shù)學(xué)分會委員。 曾任北京信息科技大學(xué)理學(xué)院院長、研工部部長兼研究生院副院長。2002年在北京應(yīng)用物理與計算數(shù)學(xué)研究所獲博士學(xué)位，主要從事計算數(shù)學(xué)研究，已在Numer Math, JCP等國內(nèi)外高水平學(xué)術(shù)期刊發(fā)表論文數(shù)十篇。