第二届偏微分方程高效数值算法研讨会

主办单位：四川师范大学数学科学学院

会议日程安排

2023年6月28日至2023年6月30日，四川师范大学，成都

一、  住宿安排及交通指引

住宿地点：维也纳国际酒店（四川师范大学店）

酒店地址：锦江区静宁路12号

酒店电话：028-62150666

会议地点：维也纳酒店肖邦会议室（二楼）

交通指引：

1.    天府国际机场

维也纳国际酒店，高速约55公里

网约车或出租车，车程约45分钟

2.    双流国际机场

维也纳国际酒店，高速约18公里

网约车或出租车，车程约20分钟

3.    火车东站

维也纳国际酒店，约5公里

网约车或出租车，车程约10分钟

二、  联系人

李鸿亮  lhl@sicnu.edu.cn  15201189828

三、  会议日程

6月28日（周二）

14：00-22：00，会议报到，酒店一楼大厅办理入住

晚餐时间18：30

6月29日（周三）（维也纳酒店二楼肖邦会议厅）

8:25 - 8:30  开幕式

主持人：周爱辉

8:30 - 9:15   李若（北京大学）

Efficient Preconditioning for Discontinuous Galerkin Method with Reconstructed Discontinuous Approximation

9:15 - 10: 00  邵嗣烘（北京大学）

Computational quantum mechanics in phase space—An attempt to break the curse of dimensionality

10: 00 - 10: 20  会间休息

主持人：明平兵

10: 20-11: 05  周爱辉（中国科学院数学与系统科学研究院）

酉算法

11:05-11:50   唐庆粦（四川大学）

Numerical methods on simulating dynamics of the nonlinear Schrodinger equation with rotation and/or nonlocal interactions

12: 00 – 14:30  午餐及午休

主持人：谢小平

14:30-15:15  明平兵（中国科学院数学与系统科学研究院）

An overview on the robust strain gradient finite elements

15:15-16:00  卢朓（北京大学）

脚踏实地，逆数而行—北太天元数值计算通用软件介绍

16:00-16:20  会间休息

主持人：李鸿亮

16:20-17:05  谢小平（四川大学）

Convergence analysis of spatial / temporal semi-discretizations for backward semilinear stochastic parabolic equations

17:05-17:50  周冠宇（电子科技大学）

The numerical methods for the coupled fluid flow under the leak interface condition of the friction-type

18:00  晚餐

6月30日，自由活动，离会

四、  报告题目及摘要（按报告先后顺序）

报告人：李若（北京大学）

题目：Efficient Preconditioning for Discontinuous Galerkin Method with Reconstructed Discontinuous Approximation

报告人：邵嗣烘（北京大学）

题目：Computational quantum mechanics in phase space—An attempt to break the curse of dimensionality

摘要：As a permanent goal and a tireless direction of computational mathematics, developing an accurate and stable high-dimensional solver has been attracting more and more attentions in recent years due to the urgent need in e.g., quantum science and high energy density physics. This talk represents our preliminary attempts to break the curse of dimensionality (CoD) which poses a fundamental obstacle to high-dimensional numerical simulations. More specifically, we will report some recent progress in both grid-based deterministic and particle-based stochastic methods for simulating high-dimensional Wigner quantum dynamics. A massively parallel solver, termed the characteristic-spectral-mixed (CHASM) scheme, is proposed to evolve the Wigner-Coulomb system in 6-D phase space. Within particle-based stochastic simulations, CoD, causing the unattainable exponential wall, reappears as the numerical sign problem. To this end, we propose a SPA (Stationary Phase Approximation) + SPADE (Sequential-clustering Particle Annihilation via Discrepancy Estimation) strategy is to overcome the numerical sign problem where it has been translated into a NP-hard problem that may have approximate solutions. Simulations of the proton-electron couplings in 6-D and 12-D phase space demonstrate the accuracy and the efficiency of our particle-based stochastic methods.

报告人：周爱辉（中国科学院数学与系统科学院）

题目：酉算法

摘要：我们将在本报告中扼要地介绍我们提出的一类收敛的保正交性（酉结构）迭代算法—酉算法，并以电子结构计算为例展示该保酉结构迭代法之潜力。

报告人：唐庆粦（四川大学）

题目：Numerical methods on simulating dynamics of the nonlinear Schrodinger equation with rotation and/or nonlocal interactions

摘要：In this talk, we will present efficient numerical methods for simulating dynamics of the nonlinear Schrodinger equation (NLSE) with nonlocal potential and rotation term. The method consists two main merits: (i) a rotating Lagrangian coordinate transformation will be presented to eliminate the rotation term.  (ii) a Kernel Truncation methods will then be presented to evaluate nonlocal potential.

报告人：明平兵（中国科学院数学与系统科学院）

题目：An overview on the robust strain gradient finite elements

报告人：卢朓（北京大学）

题目：脚踏实地，逆数而行—北太天元数值计算通用软件介绍

摘要：北太天元数值计算通用软件（以下简称“北太天元”）是在北京大学数学科学学院、北京大学大数据分析与应用技术国家工程实验室、北京大学重庆大数据研究院的指导和支持下，由北京大学重庆大数据研究院基础软件科学研究中心研发的首款具有完全自主知识产权的国产通用型科学计算软件。北太天元聚焦科学计算领域“卡脖子”问题的解决，实现了科学计算领域根技术的突破。软件具备强大的底层数学函数库，可提供科学计算、可视化、交互式程序设计功能，支持数值计算、数据分析、数据可视化、数据优化、算法开发等场景，并通过SDK与API接口，扩展支持各类学科与行业应用。目前软件已更新至V2.3，已有300余所高校、100余所企事业单位开展试用，用户数量超过3万人，曾获中央电视台等权威媒体报道。

报告人：谢小平（四川大学）

题目：Convergence analysis of spatial / temporal semi-discretizations for backward semilinear stochastic parabolic equations

摘要：We study the convergence of a spatial semidiscretization and  three temporal semi-discretizations for  backward semilinear stochastic evolution equations. Under the derived higher regularity of the transposition solution, we obtain the first-order spatial accuracy for the spatial semidiscretization that uses the standard continuous piecewise linear finite element method. We apply the theoretical results to a stochastic linear quadratic control problem. As for the three temporal semi-discretizations, we establish the convergence of the first two temporal semi-discretizations, and derive an explicit convergence rate for the third temporal semi-discretization. We apply the third temporal semi-discretization to a general stochastic linear quadratic control problem and derive an explicit convergence rate. We provide some numerical results.

报告人：周冠宇（电子科技大学）

题目：The numerical methods for the coupled fluid flow under the leak interface condition of the friction-type

摘要：The friction-type (or called barrier-type) leak interface condition (FLIC) is proposed to model the viscous fluid through a perforated membrane with a threshold permeability, where the flow passes through the perforations only when the stress difference on the membrane is above a threshold. This work establishes a comprehensive study of several numerical approaches for the Stokes/Stokes coupled flow under the FLIC, including the projection, regularization (or called penalty), and domain decomposition methods.