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RBF collocation methods for the solution of fourth order boundary value problems

来源:力学与工程学院  作者:马晓梅     日期:2019/6/3 16:19:05   点击数:915  

时间:2019-06-11 10:00

地点:九里1号综合楼240

报告人:陈清祥

 

个人简介:

陈清祥教授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身教授,担任SCI源刊物《Journal of Computers》、《Materials and Continua》的主编,SCI源刊物《Journal of Engineering Analysis with Boundary Elements》的副主编和其它六个SCI源刊物的编委。首次提出并将基本解方法应用于非齐次方程的数值模拟;首次提出了Kansas类的基本解方法用于模拟齐次方程;陈教授完成的著作“Discrete projection method”被认为构建了数学与工程应用之间的桥梁。陈清祥教授发表学术论文100余篇,出版数值计算方面的专著3部,其中《The Method of Fundamental Solutions-A Meshless Method》是第一本关于基本解方法研究的专著,它对于基本解方法的发展有着里程碑的意义。

 

讲座内容:

We apply radial basis function (RBF) collocation methods to fourth order boundary value problems (BVPs). In particular, we consider the classical Kansa method and the method of approximate particular solutions (MAPS). The novelty of the proposed approach is the inclusion of so-called ghost points which are located outside the domain of the problem under consideration. The inclusion of these points is shown to improve the accuracy and the stability of the collocation methods. An appropriate value of the shape parameter in the RBFs used is obtained using either the leave-one-out cross validation (LOOCV) algorithm or Franke's formula. The results of several numerical experiments are presented and analyzed.


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