学术报告二十四:康红梅—An Economical Representation of PDE Solution by using Compressive Sensing Approach

发布时间:2019-07-29

报告时间:2019年7月31日(星期三) 10:00-11:00

报告地点:翡翠科教楼A座1710

康红梅 副教授

工作单位:苏州大学 

报告人简介

康红梅,苏州大学数学学院副教授。2009从吉林大学数学学院毕业,同年保送至中国科学技术大学数学学院计算数学方向攻读博士,导师为陈发来教授。2016年3月至2017年3月在意大利国家研究所 CNR-IMATI从事博士后研究,合作导师为Annalisa Buffa。主要研究领域为计算机辅助几何设计 (CAGD)、几何建模、样条函数逼近、图像处理等。近年来开始关注机器学习,主要研究兴趣是借助于深度学习技术解决传统CAGD和几何建模中的问题。

报告简介

We introduce a redundant basis for numerical solution to the Poisson equation and find a sparse solution to the PDE by using a compressive sensing approach. That is, we refine a partition of the underlying domain of the PDE several times and use the multi-level nested spline subspaces over these refinements to express the solution of the PDE redundantly. We then use a compressive sensing algorithm to find an economical representation of the spline approximation of the PDE solution. The number of nonzero coefficients of an economical representation is less than the number of the standard spline representation over the last refined partition, i.e. finite element solution while we will show that the error of the spline approximation with an economical representation is the same to the standard FEM solution. This approach will be useful, e.g. in the situation when the PDE solver has a much powerful computer than the users of the solution.