报告一题目: An improved two--step MPS--MFS ghost point method with effective condition number
报告一时间：2024年04月11日9:00-10:30（北京时间）
报告一地点：线上腾讯会议（ID: 377-222-999）
报告二题目: On selecting a suitable shape parameter for RBF interpolation problems
报告二时间：2024年04月11日10:30-12:00（北京时间）
报告二地点：线上腾讯会议（ID: 377-222-999）
报告人：陈清祥(C.S. Chen)教授, University of Southern Mississippi, USA
主办单位：力学与工程科学学院固体力学研究所
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报告一简介：In this talk, we proposed to apply the newly developed effective condition number (ECN) as a tool for the optimization of the method of particular solutions (MPS) using MQ radial basis function enhanced by the ghost point method and the method of fundamental solutions (MFS). Based on the ECN, an effective numerical procedure has been proposed for the optimal determination of the shape parameter of MQ-radial basis function, the radius of fictitious circle/sphere, and the source location of the MFS. Five numerical examples are given to show the effectiveness of the proposed approach.
报告二简介：Radial basis functions (RBFs) are powerful tools for interpolation and solving PDEs, but their performance hinges on a critical parameter: the shape parameter. This talk explores methods to find the optimal shape parameter for interpolation with RBFs.We'll discuss common issues caused by a poor choice of shape parameter and introduce techniques like LOOCV and RECV to determine the optimal value. The talk will compare these methods and highlight considerations for selecting the best approach based on your problem.Researchers and scientists can ensure accurate and stable RBF applications by understanding the shape parameter's impact and optimization techniques.
报告人简介：C.S. Chen教授，1988年6月博士毕业于美国路易斯安那大学拉法叶分校，目前为美国南密西西比大学终生教授，长期从事无网格数值方法的研究。C.S. Chen教授比较有代表性的学术成就在于首次提出并将基本解方法应用到非齐次方程的数值计算，首次提出Kansa类的基本解方法并用于模拟非齐次方程。C.S. Chen教授完成的著作“Discrete projection method”被计算力学界认为是架起了数学与工程应用之间的桥梁，其完成的关于基本解方法的综述性的文章是该领域最高引文章之一。因为其研究的领先和丰硕的成果，C.S. Chen教授在无网格方法，如基本解法，特解法，径向基函数配点法等研究领域享有极高声誉。C.S. Chen教授目前发表SCI论文超过150篇，完成编写英文专著4本，引用率超过了8500多次，目前担任Engineering Analysis with Boundary Elements 和Journal of Advances in Applied Mathematics and Mechanics的副主编，多次被邀请参加多个SCI期刊的特刊编辑，是目前全世界无网格数值模拟方面的权威专家。
