报告题目：A Fast Algorithm Based on a k-th Degree Polynomial Approximation for the Caputo Fractional Derivative

时间与地点：12月14日上午9:00 － 10:00；理科楼112

报告人：黄记祖博士，中国科学院数学与系统科学研究院

摘要:

In the talk, we introduce a fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of u'(t) with the kernel (tn-s)-a. In the fast algorithm, the interval [0,tn-1] is split into several  nonuniform subintervals.  The number of the subintervals is in the order of logn at the n-th time step. The fractional kernel function is approximated by a polynomial function of K-th degree with a uniform absolute error on each subinterval. We save K+1 integrals on each subinterval, which can be written as a convolution of u'(t) with a polynomial base function. As compared with the direct method, the proposed fast algorithm reduces the storage requirement and computational cost from O(n) to O((K+1)logn) at the n-th time step. We prove that the convergence rate of the fast algorithm is the same as the direct method even a high order method is considered. The convergence rate and efficiency of the fast algorithm are illustrated via several numerical examples, including nonlinear test case with graded meshes.

报告人简介：

黄记祖, 男，1982 年8 月4 日出生于湖南省攸县，2012 年在中国科学院科学与工程计算研究所获博士学位（硕博连读），导师：曹礼群研究员。2012 至2014 年在中国科学院软件研究所从事博士后研究工作。2014 年至今，任中国科学院数学与系统科学研究院助理研究员。曾参与科技部973 课题《材料与结构一体化的热力耦合多尺度模型与算法》（批准号：2010CB832702, 2010.9-2014.9)。现主持基金委青年基金项目《基于格子Boltzmann 方程的多尺度模型与并行算法》（批准号：11501554）。独立与合作发表论文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。