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加拿大阿尔伯塔大学Yau Shu Wong教授学术报告通知

报告题目:Is pollution effect avoidable for multi-dimensional Helmholtz Equation?

:Yau Shu Wong教授,加拿大阿尔伯塔大学数学与统计学院

报告时间:6月23日(周五)上午 10:00 -12:00

报告地点:理学院214会议室

:聂玉峰教授

报告简介:Helmholtz equation arises in many problems related to wave propagations, such as acoustic, electromagnetic wave scattering and in geophysical applications. Developing efficient and highly accurate numerical schemes to solve Helmholtz equation at large wave numbers is a very challenging scientific task and it has attracted a great deal of attention for a long time. The foremost difficulty in solving Helmholtz equation numerically is to eliminate or minimize the pollution effect which could lead to a serious problem as the wave number increases. Let k, h, and n denote the wave number, the grid size and the order of a finite difference or finite element approximations, it can be showed that the relative error is bounded by k^s(kh)^n where s=2 or 1 for a finite difference or finite element method. It has been reported that it is impossible to eliminate the pollution effect that in two and more space dimensions. Recently, new finite difference schemes are developed for one-dimensional Helmholtz equation with constant wave numbers, and it has been verified that error estimate is bounded by h^{2n-1}(kh) and the convergence is independent of the wave number k even when kh >1. In this talk, we extend the idea on constructing the pollution –free difference schemes to multi-dimensional Helmholtz equation in the polar and spherical coordinates. The superior performances of the new schemes are validated by comparing the numerical solutions with those obtained by the standard finite difference and the fourth-order compact schemes. The new scheme can also be applied to certain problems in a rectangular domain.

 

 

报告题目:Data sciences and its applications to real world problems

:Yau Shu Wong教授,加拿大阿尔伯塔大学数学与统计学院

报告时间:6月26日(周一)上午:10:00-12:00

报告地点:理学院383会议室

邀 请 人:聂玉峰教授

报告简介:With the rapid advances in computer and data storage technologies, massive data have now been routinely recorded in every sector ranging from science, engineering, medical research, business and social networking, etc. Although the technology enables us to collect and to process large amount of data at high frequency rate, we are still lagging a clear understanding of what is the best way to utilize the available data and how to extract important information and feature from the data set. It should be noted that in addition to artificial intelligent and machine learning, solid knowledge in mathematical and statistical sciences also play an important role in the study of data sciences and its applications to solve real world problems. In this presentation, I review our work on utilizing real data for three practical applications:

(1) Classification in toxicity assessment

(2) Prediction for nonlinear behavior in aeroelastic systems

(3) Designing an intelligent sprinkler system

References:

1. Machine learning algorithms for mode-of-action classification in toxicity assessment, in BioData Mining, 2016

2. Structural Nonlinearity Identification and Steady-State Behavior Prediction from Transient Aeroelastic Data, presented at the NATO Specialists’ meeting in Advanced Methods in Aeroelasticity, 2008

报告人简介:Yau Shu Wong,加拿大阿尔伯塔大学数学与统计学院教授、博士生导师。1978年毕业于英国牛津大学,获理学博士学位。主要研究科学和工程中实际问题的数值计算以及算法实现的精确及有效性,尤其是空气动力学和空气弹性动力学等领域。目前从事的研究内容为数据挖掘技术对非线性工程动力学问题的预测和特征提取等方面的应用。

欢迎各位老师和同学参加!

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