题目：Numerical methods for PDEs-constrained optimal control problem in random domains

主讲人：冯梦雅副研究员

时间：2024年12月1日11:00-12:00

地点：文理大楼723

报告摘要：

PDEs in random domains appear in many applications, such as manufacturing of nanodevices, surface imaging, and biology. While many researchers have studied the numerical methods of such problems, there has been less research on the PDEs-constrained optimal control problem in random domains. Thus, we investigate the optimal control problem governed by elliptic or parabolic PDEs in random domains. By introducing a random mapping, we transform the original problem in the random domain into the stochastic problem in the fixed domain. We use the stochastic perturbation method to solve the transformed problem, and establish the decoupled first-order and second-order optimality systems, respectively. Finally, the error analyses are performed for the first-order and second-order schemes, and some examples are provided to verify the theoretical results.

个人简介：

冯梦雅，南京林业大学应用数学系副研究员，2024年6月博士毕业于山东大学计算数学专业，7月加入南京林业大学理学院。研究方向为随机偏微分方程约束的最优控制问题。在Comput. Optim. Appl., Appl. Numer. Math., Comput. Appl. Math. 等