報告題目：A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger Equations
報 告 人：劉洋 教授 内蒙古大學數學科學學院
報告時間：2020 年11 月19日上午 10:50-11:30
報告地點：騰訊會議 ID：892 255 965
會議密碼：1119
校内聯系人：呂俊良 lvjl@jlu.edu.cn
報告摘要：
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.
報告人簡介：
劉洋，内蒙古大學數學科學學院教授、博士生導師，兼任中國數學會計算數學分會理事。2017.7-2018.7于澳大利亞昆士蘭科技大學公派訪問學者和不定期于北京計算科學研究中心訪問。主要從事微分方程與分數階微分方程的标準有限元方法、混合元方法、有限差分方法及間斷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”等期刊發表多篇學術論文，分别在國防工業出版社和西安電子科技大學出版社出版專著兩部。目前主持在研或結題3項國家自然科學基金等多個項目。入選自治區‘草原英才’工程青年創新創業人才一層次。
