讲座题目：时间分布阶和Riesz空间分数扩散波方程的快速二阶隐式差分格式

主 讲 人：顾先明博士

讲座时间：2018年12月14日9:45-10:45

讲座地点：钱伟长楼 201会议室

讲座内容简介：

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.

主讲人简介：

顾先明博士，现任职于西南财经大学经济数学学院，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。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。