报告题目：Convergence analysis of LMM and DDMs for a parabolic inverse Robin problem
报告人：蒋代军 副教授
邀请人：姚青云
报告时间：2023年10月24日（周二）下午16:00-17:00
报告地址：腾讯会议（会议号：918-684-428）
报告摘要：In this talk, we study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in parabolic systems. The L-M method transforms the Tikhonov regularized nonlinear non-convex minimizations into convex minimizations. And the quadratic convergence of the L-M method is rigorously established for the nonlinear parabolic inverse problems for the first time, under a simple novel adaptive strategy for selecting regularization parameters during the L-M iteration. Then the domain decomposition methods are used to solve the convex minimizations. The methods are completely local and the local minimizers have explicit expressions within the subdomains. Numerical experiments are presented to show the accuracy and efficiency of the methods, in particular, the convergence seems nearly optimal in the sense that the iteration number of the methods is independent on the mesh size.
报告人简介：蒋代军，华中师范大学副教授，博士生导师，2007年获得华中师范大学学士学位，2009年和2012年分别获得武汉大学硕士和博士学位。蒋代军博士的研究领域包括偏微分方程反问题、稀疏优化及控制，快速算法等，主持国家自然科学基金项目4项，在SIAM 系列、 Inverse Problems等刊物上发表学术论文近30篇。
数学与统计学院
2023年10月23日