报告承办单位: 数学与统计学院

报告题目:  A numerical scheme for the time-fractional diffusion equation by layer potentials with applications to inverse problems

报告内容:  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.

 报告人姓名:  王海兵

报告人所在单位: 东南大学数学学院

报告人职称/职务及学术头衔:  教授

报告时间:  2021年12月04日11:00-11:40

报告地点: 卡斯迪漫享酒店二楼VIP会议厅

报告人简介:  王海兵，男，教授，博士研究生导师，主要从事数学物理反问题的研究。2012年获得北海道大学和东南大学的理学博士学位，2014年获得江苏省优秀博士学位论文，2016年入选江苏高校“青蓝工程”中青年学术带头人培养对象，2017年作为第二完成人获得教育部自然科学二等奖，2018年获得江苏省工业与应用数学学会第二届“工业与应用数学奖青年奖”。现任中国数学会计算数学分会常务委员。主持三项国家自然科学基金和一项江苏省自然科学基金，在SIAP, SIAM-MMS, IP, JCP等国内外刊物上发表三十余篇学术论文，多次访问东京大学、北海道大学、仁荷大学和奥地利科学院RICAM，受邀在国际学术会议上作报告十余次。