学术报告：2018/12/13，15:00-16:00，顾先明，西南财经大学，格罗宁根大学

报告人

顾先明

单位

西南财经大学，格罗宁根大学

报告题目

Fast second-order implicit difference   schemes for time distributed-order and Riesz space fractional diffusion-wave   equations

报告时间

2018/12/13

15:00-16:00

地点

bevictor伟德官网第一报告厅

邀请人

孙志忠

报告摘要

In this talk, fast numerical   methods are established for solving a class of time distributed-order and   Riesz space fractional diffusion-wave equations. We derive new difference   schemes by the weighted and shifted Grünwald formula in time and the   fractional centered difference formula in space. The unconditional stability   and second-order convergence in time, space and distributed-order of the   difference schemes are analyzed. In the one-dimensional case, the   Gohberg-Semencul formula utilizing the preconditioned Krylov subspace method   is developed to solve the symmetric positive definite Toeplitz linear systems   derived from the proposed difference scheme. In the two-dimensional case, we   also design a global preconditioned conjugate gradient method with a   truncated preconditioner to solve the discretized Sylvester matrix equations.   We prove that the spectrum of the preconditioned matrices in both cases are   clustered around one, such that the proposed numerical methods with   preconditioners converge very quickly. Some numerical experiments are carried   out to demonstrate the effectiveness of the proposed difference schemes and   show that the performances of the proposed fast solution algorithms are   better than other numerical methods.

报告人简介

顾先明博士，现任职于西南财经大学经济bevictor伟德官网，数学研究所副所长、硕士生导师。2017年在电子科技大学获得博士学位，2014-2016年获得荷兰格罗宁根大学Ubbo Emmius博士奖学金资助赴该校攻读第二学位，2014-2016年连续三年获得博士研究生国家奖学金，2014年还获得“成电杰出员工（研究生）”称号。主要研究方向为数值线性代数、高性能科学计算和分数阶微分方程快速数值解等。截止目前，已在国际SCI期刊上发表学术论文34篇，ESI高被引文章1篇，其中包括IEEE Trans. Microw.   Theory Techn., Comput. Phys. Commun., J. Comput. Phys., J. Sci. Comput.等国际知名SCI期刊，还参与编写和出版学术专著一部。另外，长期担任15本国际SCI期刊的匿名审稿人，并先后获得SCI期刊Comput. Math. Appl.,   Appl. Numer. Math.和Math. Comput.   Simulation颁发的年度最佳审稿人称号。