學(xué)術(shù)報(bào)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(shí)間：12月1日8:00-9:00

地點(diǎn)：文理大樓723

報(bào)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(jiǎn)介：

孫同軍，山東大學(xué)數(shù)學(xué)學(xué)院教授、博士生導(dǎo)師。曾在日本、加拿大和英國(guó)的多所大學(xué)留學(xué)和訪(fǎng)問(wèn)。現(xiàn)任中國(guó)CSIAM金融科技與算法專(zhuān)業(yè)委員會(huì)委員，山東數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)專(zhuān)業(yè)委員會(huì)委員兼秘書(shū)，中國(guó)計(jì)算物理學(xué)會(huì)計(jì)算石油地質(zhì)專(zhuān)業(yè)委員會(huì)委員，曾任中國(guó)CSIAM不確定性量化專(zhuān)業(yè)委員會(huì)委員。擔(dān)任國(guó)家和多個(gè)省份自然科學(xué)基金的通訊評(píng)審專(zhuān)家，教育部學(xué)位中心通訊評(píng)議專(zhuān)家，美國(guó)數(shù)學(xué)會(huì)Mathematical Reviews評(píng)論專(zhuān)家，計(jì)算數(shù)學(xué)領(lǐng)域多個(gè)國(guó)際知名期刊的審稿人。

目前主要研究方向?yàn)? 偏微分方程最優(yōu)控制問(wèn)題的數(shù)值方法的理論及應(yīng)用。主持國(guó)家和山東省自然科學(xué)基金項(xiàng)目等7項(xiàng)（國(guó)家自然科學(xué)基金面上項(xiàng)目2項(xiàng)，國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目子課題1項(xiàng)，山東省自然科學(xué)基金面上項(xiàng)目2項(xiàng)，山東省優(yōu)秀中青年科學(xué)家科研獎(jiǎng)勵(lì)基金1項(xiàng)，教育部留學(xué)回國(guó)人員科研啟動(dòng)基金1項(xiàng)）。作為項(xiàng)目組主要成員參加了國(guó)家和省部級(jí)項(xiàng)目10多項(xiàng),已發(fā)表SCI收錄文章50余篇。

學(xué)術(shù)報(bào)告（二）

題目：Weak Galerkin finite element method for semiconductor device simulation

主講人：高夫征 教授

時(shí)間：12月1日9:00-10:00

地點(diǎn)：文理大樓723

報(bào)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(jiǎn)介：

高夫征，山東大學(xué)數(shù)學(xué)學(xué)院教授/博士生導(dǎo)師，山東省計(jì)算數(shù)學(xué)專(zhuān)委會(huì)成員，泰山學(xué)者團(tuán)隊(duì)骨干成員（2010.06-2015.08），Review Editor in Frontiers in Physics-Statistical and Computational Physics（2022.10-）。美國(guó)阿肯色大學(xué)小石城校區(qū)訪(fǎng)問(wèn)學(xué)者。研究方向?yàn)槠⒎址匠虜?shù)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(shù)值方法的分析與應(yīng)用研究。承擔(dān)完成國(guó)家級(jí)、省部級(jí)科研項(xiàng)目十余項(xiàng)（主持完成國(guó)家自然科學(xué)基金面上項(xiàng)目、山東省自然科學(xué)基金面上項(xiàng)目、山東省優(yōu)秀中青年科學(xué)家科研獎(jiǎng)勵(lì)基金、中國(guó)博士后基金項(xiàng)目）、中石化國(guó)家科技攻關(guān)外協(xié)項(xiàng)目一項(xiàng)。現(xiàn)主持國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目子課題一項(xiàng)，在國(guó)際知名學(xué)術(shù)期刊發(fā)表SCI論文近50篇。

學(xué)術(shù)報(bào)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(shí)間：12月1日10:00-11:00

地點(diǎn)：文理大樓723

報(bào)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(jiǎn)介：

付凱，中國(guó)海洋大學(xué)數(shù)學(xué)科學(xué)學(xué)院副教授。于2012年獲得山東大學(xué)計(jì)算數(shù)學(xué)博士學(xué)位，2013年至2015年在加拿大約克大學(xué)擔(dān)任博士后研究員。研究方向?yàn)槠⒎址匠虜?shù)值解和環(huán)境數(shù)值模擬，在對(duì)流擴(kuò)散問(wèn)題計(jì)算方法和環(huán)境計(jì)算中取得了重要研究成果。在包括國(guó)際著名學(xué)術(shù)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(fā)表SCI論文20余篇。主持國(guó)家自然科學(xué)基金面上項(xiàng)目、青年基金項(xiàng)目和山東省自然科學(xué)基金面上項(xiàng)目等多個(gè)項(xiàng)目。

學(xué)術(shù)報(bào)告（四）

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

主講人：馮夢(mèng)雅 副研究員

時(shí)間：12月1日11:00-12:00

地點(diǎn)：文理大樓723

報(bào)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(jiǎn)介：

馮夢(mèng)雅，南京林業(yè)大學(xué)應(yīng)用數(shù)學(xué)系副研究員，2024年6月博士畢業(yè)于山東大學(xué)計(jì)算數(shù)學(xué)專(zhuān)業(yè)，7月加入南京林業(yè)大學(xué)理學(xué)院。研究方向?yàn)殡S機(jī)偏微分方程約束的最優(yōu)控制問(wèn)題。在Comput. Optim. Appl., Appl. Numer. Math., Comput. Appl. Math.等期刊發(fā)表論文多篇。