演讲人: 张凯 教授（吉林大学）

题目：Efficient numerical methods for Helmholtz optimal control problems with random coefficient

摘要：Efficient numerical methods for solving Poisson equation constraint optimal control problems with random coefficient are discussed in this talk. By applying the finite element method and the Monte Carlo approximation, the original optimal control problem is discretized and transformed into an optimization problem. Taking advantage of the separable structures, Algorithm 1 is proposed for solving the problem, where an alternating direction method is used. Both computational and storage costs of this algorithm are very high. In order to reduce the computational cost, Algorithm 2 is proposed, where the multi-modes expansion is introduced and applied. Further, in order to reduce the storage cost, we propose Algorithm 3 based on Algorithm 2. The main idea is that the random term is shifted to the objective functional, which could be computed in advance. Therefore, we only need to solve a deterministic optimization problem, which could reduce all the costs significantly. Moreover, the convergence analyzes of the proposed three algorithms are established, and numerical simulations are carried out to test the performances of them.

演讲人简介:张凯，吉林大学数学学院教授、博士生导师。1999年本科毕业于吉林大学数学系，2006年获吉林大学博士学位。博士论文被评为吉林省优秀博士论文。2008年获得香港中文大学联合培养博士学位，2008年至2010年赴密歇根州立大学开展博士后研究，曾先后赴伊利诺伊州立大学，奥本大学等开展合作研究。主要研究兴趣为随机偏微分方程的数值解法。主要从事SPDE控制优化问题的数值方法、期权定价、随机麦克斯韦方程和随机声波方程的研究。先后主持国家自然科学基金等项目10项，发表论文40余篇，其中SCI论文30余篇。

时间:2019年9月25日上午8:00-9：30

地点:科技楼南楼813室