A Stable Fast Time-Stepping Method for Fractional Integral and Derivative Operators

报告题目: A Stable Fast Time-Stepping Method for Fractional Integral and Derivative Operators

报告人: 曾凡海, 新加坡国立大学

报告时间和地点: 10:00-11:00, 2018年11月7号, 周三; 知新楼B1032

摘要: A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $\Delta T$ and a history part, where the local part is approximated by the direct convolution method and the history part is approximated by a fast memory-saving method. The fast method has $O(n_0+\sum_{\ell}^L {q}_{\alpha}(N_{\ell}))$ active memory and $O(n_0n_T+(n_T-n_0)\sum_{\ell}^L{q}_{\alpha} (N_{\ell}))$ operations, where $L=\log(n_T-n_0)$, $n_0={\Delta T}/\tau$, $n_T=T/\tau$, $\tau$ is the stepsize, $T$ is the final time, and ${q}_{\alpha}{(N_{\ell})}$ is the number of quadrature points used in the truncated Laguerre–Gauss (LG) quadrature. The error bound of the present fast method is analyzed. It is shown that the error from the truncated LG quadrature is independent of the stepsize, and can be made arbitrarily small by choosing suitable parameters that are given explicitly. Numerical examples are presented to verify the effectiveness of the current fast method.

报告人简介: 曾凡海, 博士毕业于上海大学,毕业后先后在美国布朗大学、澳大利亚昆士兰科技大学和新加坡国立大学做博士后,在 SIAM 数值分析和SIAM科学计算等一流计算数学期刊上发表了十多篇学术论文,合作出版专著一部, 在非局部问题数值方法的奇性处理和快速算法领域作出了具有影响力的工作,有7篇ESI高被引论文,单篇文章引用率最高达到120次, 并于2016年获得上海市优秀博士论文奖。

邀请人: 蒋晓芸