讲座主题：A numerical scheme for the time-fractional diffusion equation by layer potentials with applications to inverse problems

专家姓名：王海兵

工作单位：东南大学

讲座时间：2021年12月16日 14:50-15:50

讲座地点：腾讯会议，会议ID：403792057

主办单位：十大网投平台大全下载数学与信息科学学院

内容摘要：

In this talk, we show a numerical scheme for solving an initial-boundary value problem for the time-fractional diffusion equation. By expressing the solution as a single-layer potential, the initial-boundary value problem is transformed into a boundary integral equation for the unknown density function. To numerically solving the resulting boundary integral equation, we develop a stable discretization scheme for layer potentials. First, we rewrite the layer potential operators as generalized Abel integral operators in time. Then, the asymptotic expansions of those kernels at the initial time are derived. Consequently, we establish a stable time discretization scheme. The spatial discretization is performed by a standard quadrature rule for boundary integrals of smooth functions. Finally, we present several numerical examples to show the efficiency and accuracy of the proposed numerical scheme. Applications to inverse problems will also be discussed.

主讲人介绍：

王海兵，东南大学数学学院教授，博士研究生导师，主要从事数学物理反问题的研究。现任中国数学会计算数学分会常务理事。2012年获得北海道大学和东南大学的理学博士学位。目前正主持一项国家自然科学基金面上项目，代表性成果发表在SIAM系列刊物，IP，JCP，JDE等国际知名刊物上。