學術報告（一）

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

主講人：孫同軍 教授

時間：12月1日8:00-9:00

地點：文理大樓723

報告摘要：

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.

主講人簡介：

孫同軍，山東大學數學學院教授、博士生導師。曾在日本、加拿大和英國的多所大學留學和訪問。現任中國CSIAM金融科技與算法專業委員會委員，山東數學會計算數學專業委員會委員兼秘書，中國計算物理學會計算石油地質專業委員會委員，曾任中國CSIAM不確定性量化專業委員會委員。擔任國家和多個省份自然科學基金的通訊評審專家，教育部學位中心通訊評議專家，美國數學會Mathematical Reviews評論專家，計算數學領域多個國際知名期刊的審稿人。

目前主要研究方向為: 偏微分方程最優控制問題的數值方法的理論及應用。主持國家和山東省自然科學基金項目等7項（國家自然科學基金面上項目2項，國家自然科學基金重點項目子課題1項，山東省自然科學基金面上項目2項，山東省優秀中青年科學家科研獎勵基金1項，教育部留學回國人員科研啟動基金1項）。作為項目組主要成員參加了國家和省部級項目10多項,已發表SCI收錄文章50余篇。

學術報告（二）

題目：Weak Galerkin finite element method for semiconductor device simulation

主講人：高夫征 教授

時間：12月1日9:00-10:00

地點：文理大樓723

報告摘要：

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.

主講人簡介：

高夫征，山東大學數學學院教授/博士生導師，山東省計算數學專委會成員，泰山學者團隊骨干成員（2010.06-2015.08），Review Editor in Frontiers in Physics-Statistical and Computational Physics（2022.10-）。美國阿肯色大學小石城校區訪問學者。研究方向為偏微分方程數值方法，尤其是弱Galerkin有限元法、間斷Galerkin有限元法、有限體積法等數值方法的分析與應用研究。承擔完成國家級、省部級科研項目十余項（主持完成國家自然科學基金面上項目、山東省自然科學基金面上項目、山東省優秀中青年科學家科研獎勵基金、中國博士后基金項目）、中石化國家科技攻關外協項目一項。現主持國家自然科學基金重點項目子課題一項，在國際知名學術期刊發表SCI論文近50篇。

學術報告（三）

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

主講人：付凱副 教授

時間：12月1日10:00-11:00

地點：文理大樓723

報告摘要：

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.

主講人簡介：

付凱，中國海洋大學數學科學學院副教授。于2012年獲得山東大學計算數學博士學位，2013年至2015年在加拿大約克大學擔任博士后研究員。研究方向為偏微分方程數值解和環境數值模擬，在對流擴散問題計算方法和環境計算中取得了重要研究成果。在包括國際著名學術期刊《SIAM J Sci Comput》、《J Comput Phys》、《J Sci Comput》、《Atmos Environ》、《J Atmos Ocean Tech》和《Atmos Res》等期刊發表SCI論文20余篇。主持國家自然科學基金面上項目、青年基金項目和山東省自然科學基金面上項目等多個項目。

學術報告（四）

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

主講人：馮夢雅 副研究員

時間：12月1日11:00-12:00

地點：文理大樓723

報告摘要：

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.

主講人簡介：

馮夢雅，南京林業大學應用數學系副研究員，2024年6月博士畢業于山東大學計算數學專業，7月加入南京林業大學理學院。研究方向為隨機偏微分方程約束的最優控制問題。在Comput. Optim. Appl., Appl. Numer. Math., Comput. Appl. Math.等期刊發表論文多篇。