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  • 杭州電子科技大學·計算機學院


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    閱讀量:472 發布時間:2019-07-04 09:05:25



    報告人:蘇州大學 康紅梅博士

    主題:An Economical Representation of PDE Solution by using Compressive Sensing Approach




    康紅梅,蘇州大學數學學院副教授。2009 吉林大學數學學院畢業,年保送至中國科學技術大學數學學院計算數學方向攻讀博士,導師為陳發來教授。2016 3月至 2017 3月在意大利國家研究所 CNR-IMATI從事博士后研究,合作導師為Annalisa Buffa。主要研究領域為計算機輔助幾何設計 (CAGD)、幾何建模、樣條函數逼近、圖像處理等。近年來開始關注機器學習,主要研究興趣是借助于深度學習技術解決傳統CAGD和幾何建模中的問題。




    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