报告题目：Newton's method and its hybrid with machine learning for Navier-Stokes Darcy Models discretized by mixed element methods

报告人：彭辉 副教授 南京理工大学数学与统计学院

报告时间：2025年9月12日下午14:00-15:00

报告地点：腾讯会议：#腾讯会议：819-852-136

校内联系人：张剑桥 [email protected]

报告摘要：In this talk, we focus on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the relative discretized problem. It is proved technically that this method converges quadratically with the convergence rate independent of the mixed element mesh size, under certain standard conditions. Later on, a deep learning algorithm is proposed for solving this nonlinear coupled problem. Furthermore, an Int-Deep algorithm is constructed by combining the previous two methods so as to further improve the computational effciency and robustness. A series of numerical examples are reported to show the numerical performance of the proposed methods.

报告人简介：彭辉, 博士, 南京理工大学副教授, 主要从事非标准有限元方法的分析和应用方面的研究, 主持国家自然科学基金青年基金一项, 在Sci.China Math., Commun. Comput. Phys., J. Comput.Math等杂志发表学术论文十余篇.