讲座题目：High order fast algorithm with almost optimum memory for the Caputo fractional derivative

讲座时间：

2017年6月15日（周四）上午10:00-12:00

讲座地点：南教一120

主讲人：  黄记祖 副研究员

摘要：We present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of u′(t) with the kernel (t_n - t)^( -α). The algorithm is based on a split of the interval [0, t_n] and a polynomial approximation of the special function (1 - t) ^( -α) on the interval [- 1/3, 1/ 3] with absolute error ϵ_K. The number of the subintervals is of the order log n at the n-th time step. As compared with the direct method, the proposed algorithm reduces the storage requirement from O(n) to O(log n). We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order direct method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples.

报告人简介：

黄记祖，中国科学院计算数学与科学工程计算研究所，副研究员。2012年在中国科学院计算数学与科学工程计算研究所获博士学位（硕博连读），2012至2014年在中国科学院软件研究所从事博士后研究工作。曾参与科技部973课题，现主持一项国家自然科学基金。在Multiscale Model. and Simul和SIAM J. Sci. Comput.等期刊发表论文10篇，主要研究领域为多尺度模型和并行算法的设计与相关软件的开发，涉及计算材料科学、计算流体力学和计算传热学等领域的建模和计算。