报告题目：A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger Equations

报 告 人：刘洋 教授 内蒙古大学数学科学学院

报告时间：2020 年11 月19日上午 10:50-11:30

报告地点：腾讯会议 ID：892 255 965

会议密码：1119

校内联系人：吕俊良        lvjl@jlu.edu.cn

报告摘要：

     In this talk, we aim at analyzing a novel structure preserving difference scheme for the high dimensional nonlinear space-fractional Schrödinger equation. The temporal direction is discretized by the modified Crank-Nicolson scheme, while the spacial variable is approximated by formulas from the shifted convolution quadrature. The energy and mass preserving properties are proved rigorously for the scheme based on the newly developed properties of the coefficients matrix. Further, the optimal convergence rate O ( h2 +τ2 ) is derived in detail where h, τ denote the spacial and temporal mesh sizes, respectively. To save the computing cost, we consider the preconditioned fast BiCG (PF-BiCG) algorithm for the resulting complex systems. Numerical experiments are conducted to confirm our theoretical conclusions and the efficiency of the fast algorithm.

报告人简介：

    刘洋，内蒙古大学数学科学学院教授、博士生导师，兼任中国数学会计算数学分会理事。2017.7-2018.7于澳大利亚昆士兰科技大学公派访问学者和不定期于北京计算科学研究中心访问。主要从事微分方程与分数阶微分方程的标准有限元方法、混合元方法、有限差分方法及间断Galerkin方法等研究。目前在“Journal of Computational Physics”、“International Journal of Heat and Mass Transfer”、“Nonlinear Dynamics”、“Numerical Methods for Partial Differential Equations”、“Applied Mathematics Letters”、“Applied Mathematics and Computation”、“Computers & Mathematics with Applications”、“Numerical Algorithms”等期刊发表多篇学术论文，分别在国防工业出版社和西安电子科技大学出版社出版专著两部。目前主持在研或结题3项国家自然科学基金等多个项目。入选自治区‘草原英才’工程青年创新创业人才一层次。