Efficient numerical methods for Helmholtz optimal control problems with random coefficient

发布时间：2019-09-17 作者：浏览次数：

Speaker:	张凯	DateTime:	2019年9月27日下午 2：30-3：30
Brief Introduction to Speaker: 张凯，吉林大学，教授。		Place:	六号楼二楼报告厅
Abstract: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 conv...