学术报告（一）

题目：Adaptive Stochastic Numerical Methods for Elliptic Optimal Control Problem with Random Coefficient

主讲人：孙同军 教授

时间：12月1日8:00-9:00

地点：文理大楼723

报告摘要：

In this talk, we introduce the research progress on adaptive stochastic numerical methods for optimal control problem governed by elliptic equations with random coefficients. As well known, by finite-dimensional noise assumption, the model problem can be represented as deterministic equations in finite-dimensional parameter space (also named as the probability space), and then be discretized by some numerical ways both in the parameter space and the physical space. To build adaptive methods, a posteriori error estimates are needed beforehand. For the physical space, the a posteriori error estimates can be derived as usually. The main difficulty is how to derive a posteriori error estimates for the parameter space. We consider two trial ways. Based on these estimates, refinement strategies are designed, which allow to steer the adaption both in the parameter space and the physical space. Finally, the corresponding numerical examples are presented to illustrate our theoretical results.

主讲人简介：

孙同军，山东大学数学学院教授、博士生导师。曾在日本、加拿大和英国的多所大学留学和访问。现任中国CSIAM金融科技与算法专业委员会委员，山东数学会计算数学专业委员会委员兼秘书，中国计算物理学会计算石油地质专业委员会委员，曾任中国CSIAM不确定性量化专业委员会委员。担任国家和多个省份自然科学基金的通讯评审专家，教育部学位中心通讯评议专家，美国数学会Mathematical Reviews评论专家，计算数学领域多个国际知名期刊的审稿人。

目前主要研究方向为: 偏微分方程最优控制问题的数值方法的理论及应用。主持国家和山东省自然科学基金项目等7项（国家自然科学基金面上项目2项，国家自然科学基金重点项目子课题1项，山东省自然科学基金面上项目2项，山东省优秀中青年科学家科研奖励基金1项，教育部留学回国人员科研启动基金1项）。作为项目组主要成员参加了国家和省部级项目10多项,已发表SCI收录文章50余篇。

学术报告（二）

题目：Weak Galerkin finite element method for semiconductor device simulation

主讲人：高夫征 教授

时间：12月1日9:00-10:00

地点：文理大楼723

报告摘要：

This talk will report weak Galerkin finite element methods for semiconductor device simulations. Including drift-diffusion (DD) and high-field (HF) models, which involves not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. The main difficulties in the analysis include the treatment of the nonlinearity and coupling of the models. The optimal order error estimates in a discrete H1 norm and the standard L 2 norm are derived. Numerical experiments are presented to illustrate our theoretical analysis. Moreover, numerical schemes also work out for the discontinuous diffusion coefficient problems.

主讲人简介：

高夫征，山东大学数学学院教授/博士生导师，山东省计算数学专委会成员，泰山学者团队骨干成员（2010.06-2015.08），Review Editor in Frontiers in Physics-Statistical and Computational Physics（2022.10-）。美国阿肯色大学小石城校区访问学者。研究方向为偏微分方程数值方法，尤其是弱Galerkin有限元法、间断Galerkin有限元法、有限体积法等数值方法的分析与应用研究。承担完成国家级、省部级科研项目十余项（主持完成国家自然科学基金面上项目、山东省自然科学基金面上项目、山东省优秀中青年科学家科研奖励基金、中国博士后基金项目）、中石化国家科技攻关外协项目一项。现主持国家自然科学基金重点项目子课题一项，在国际知名学术期刊发表SCI论文近50篇。

学术报告（三）

题目：Mass conservative temporal second order and spatial high order characteristic finite volume methods for atmospheric pollution advection diffusion problems

主讲人：付凯副 教授

时间：12月1日10:00-11:00

地点：文理大楼723

报告摘要：

In this talk, the temporal second order mass conservative methods for solving atmospheric pollution advection diffusion problems are presented. The technique of characteristics and high order conservative interpolation are combined to provide the high order accuracy both in time and space, continuity of the discrete fluxes, as well as the preservation of quantity. The second order temporal and spatial accuracy, as well as mass conservation property are demonstrated by comparing results with exact solutions. Comparisons with standard characteristic finite difference methods show the excellent performance of our method that it can get much more stable and accurate solutions with less computational resources. The predicted results of PM2.5 concentrations in the realistic simulation are consistent with observed data in three metropolitan municipalities and the capitals of seven provinces in China. The developed high order mass-conservative characteristic method can be used to solve the large scale atmospheric pollution problems in real-world applications.

主讲人简介：

付凯，中国海洋大学数学科学学院副教授。于2012年获得山东大学计算数学博士学位，2013年至2015年在加拿大约克大学担任博士后研究员。研究方向为偏微分方程数值解和环境数值模拟，在对流扩散问题计算方法和环境计算中取得了重要研究成果。在包括国际著名学术期刊《SIAM J Sci Comput》、《J Comput Phys》、《J Sci Comput》、《Atmos Environ》、《J Atmos Ocean Tech》和《Atmos Res》等期刊发表SCI论文20余篇。主持国家自然科学基金面上项目、青年基金项目和山东省自然科学基金面上项目等多个项目。

学术报告（四）

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：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.

主讲人简介：

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.等期刊发表论文多篇。