工程建模与科学计算湖北省重点实验室自2016年12月获得认定以来已运行近2年，为了规范和科学地建设运行实验室，加快推进实验室的各项工作，实验室将于2018年11月24日-26日在华中科技大学召开2018年学术委员会会议暨偏微分方程计算与分析青年论坛,特敬请光临并作学术报告。

会议日程表

11月24日下午

注册报到（地点：华中科技大学国际学术交流中心八号楼大厅).

11月25日上午

8：30-8：45：开幕式（地点：科技楼702）

主持人：张诚坚

程序：1.数学与统计学院院长吴军教授致欢迎词2.拍照

主持人：黄乘明
报告人	时间	报告题
周爱辉	8：45-9：30	电子结构模型与计算中的若干数学问题
汤华中	9：30-10：15	Globally hyperbolic moment model of   arbitrary order for special relativistic Boltzmann equation
10：15-10：30会间休息
主持人：施保昌
黄飞敏	10：30-11：15	Compensated compactness and its application   on hyperbolic conservation laws and isometric embedding
主持人：吴军
11：15-12：00学术委员会讨论实验室发展

11月25日下午

地点：科技楼702

主持人：汤华中
报告人	时间	报告题
明炬	14：30-15：00	Adaptive Dynamically ROM and Its   Applications
柴振华	15：00-15：30	多相多组分流体系统的格子Boltzmann方法
15：30-15：50会间休息
主持人：黄飞敏
李东方	15：50-16：20		Linearized Galerkin FEMs for nonlinear time   fractional parabolic problems with non-smooth solutions
张一威	16：20-16：50		Understanding physical mixing processes via   transfer operator approach

11月26日上午

会议闭幕，离会

学术报告摘要

电子结构模型与计算中的若干数学问题

周爱辉

中国科学院数学与系统科学研究院

第一原理电子结构计算已成为理解和探索物质机理以及预测材料性质的重要手段与工具.它可以解释实验,与实验相辅相成,从而能加速新材料的发现与设计.尤其是第一原理计算还可能替代极端条件下的实验.如何又快又好地计算大规模的电子结构是极具挑战性的课题.而电子结构模型及其数学基础与数学性质在理解、分析与设计第一原理电子结构计算方法中发挥着重要作用.我们将介绍我们小组在电子结构模型的数学基础和电子结构计算的方法与理论的研究中关注的若干数学问题.

Globally hyperbolic moment model of arbitrary order for special relativistic Boltzmann equation

汤华中

北京大学数学科学学院

his work extends the model reduction method by the operator projection to the special relativistic Boltzmann equation. In 3D, the key is that the real spherical harmonics are used to replace the irreducible tensors used in the literature, and the product of infinite families of the complicate Grad type orthogonal polynomials depending on a parameter and the real spherical harmonics is used to construct the basis of the weighted polynomials space. Their complicate properties are also carefully studied, including their recurrence relations, their derivatives with respect to the independent variable and parameter, and the zeros of the orthogonal polynomials. Based on our theoretical analysis, the globally hyperbolic moment model of arbitrary order for the special relativistic Boltzmann equation, and its properties can be derived, including the global hyperbolicity, linearly stability and Lorentz covariance. Moreover, the quasi-one-dimensional case, the non-relativistic limit, and the ultra-relativistic limit case are also discussed.

Compensated compactness and its application on hyperbolic conservation laws and isometric embedding

黄飞敏

中国科学院数学与系统科学研究院应用数学研究所

In this lecture, i will present our recent work on the global existence of entropy solutions for the multi-dimensional compressible Euler equations, including steady solutions and spherically symmetry solutions with the help pf the theory of compensated compactness. I will also introduce some results on the isometric embedding through Gauss-Codazzi equation.

Adaptive Dynamically ROM and Its Applications

明炬

华中科技大学

We explore the dynamically bi-orthogonal (DyBO) method to solve the stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder. To describe the channel flow, we adopt the time dependent Navier Stokes equations with open boundary condition, and assume the inlet flow and the rotation speed of the cylinder have stochastic perturbations. In this optimal control problem, the control variable is the rotation speed of the cylinder, which is adjusted to achieve the objectives. For solving the optimal rotation speed of the cylinder, we use the effective gradient-based optimization algorithm to solve the optimality systems. If we use the classical Monte Carlo (MC) method to deal with the stochastic parts in the gradient-based optimization algorithm, the computational cost is unaffordable. The polynomial chaos expansions (PCE) method is a wise choice to reduce the cost, but it still spends high computational cost as the number of expansion terms increase quickly if more accurate solutions are required. We adopt the DyBO method to reduce the computational cost with the same accuracy as MC method, which bases on the Karhunen-Loeve expansion (KLE) that gives the sparsest representation of the stochastic solutions. To overcome the difficulty of calculating the pressure in the performance of the DyBO method, we combine the pressure Poisson equation (PPE) method with the DyBO method. Numerical tests are performed to validate our methodology.

多相多组分流体系统的格子Boltzmann方法

柴振华

华中科技大学

本报告将主要围绕多相多组分流体系统的格子Boltzmann方法，重点介绍其模型构建，高效算法设计以及在实际问题中的一些应用。最后，报告还将简要介绍该方法的一些最新进展及存在的一些问题。

Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions

李东方

华中科技大学

In this talk, a Newton linearized Galerkin finite element method is proposed to solve nonlinear time fractional parabolic problems with non-smooth solutions. Iterative processes or corrected schemes become dispensable by the use of the Newton linearized method and graded meshes in the temporal direction. The optimal error estimate in the $L^2$-norm is obtained without any time step restrictions dependent on the spatial mesh size. Such unconditional convergence results are proved by including the initial time singularity into concern, while previous unconditional convergent results always require continuity and boundedness of the temporal derivative of the exact solution. Numerical experiments are conducted to confirm the theoretical results.

Understanding physical mixing processes via transfer operator approach

张一威

华中科技大学

Industrial and chemical mixing processes of various kinds occur throughout nature and are vital in many technological applications. In the context of discrete dynamical systems, the transfer operator approach has been shown as a powerful tools from both theoretic and numerical viewpoint. In this talk, I will use a toy model (i.e., the one dimensional stretch and fold map) as an example to provide a brief introduction on the relationships between the spectral properties of the associated transfer operator and the estimations of the optimal mixing rate of the mixing process. Moreover, I will address how the optimal mixing rate varies according to the stretch and fold map has cutting and shuffling behaviour (i.e., composing with a permutation).