报告题目：A Modified Method of Approximate Particular Solutions for Solving PDEs
报 告 人: C.S. Chen （美国南密西西比大学）
In this talk, the method of approximate particular solutions (MAPS) is modified using polyharmonic splines (PS) as the basis function. In the original MAPS, integrated RBFs, so called particular solutions, are used. An additional integrated polynomial basis is added when PS is used. In the modified MAPS, an additional polynomial basis is directly added to the integrated RBFs without integration. It is remarkable that MAPS becomes extremely accurate when we use the PS kernels in the proposed method. Another advantage is that there is no shape parameter to be taken care of in PS. The results from the modified MAPS with PS can be improved by simply increasing the order of PS or the number of collocation points. Other RBFs such as MQ can be utilized in the modified MAPS as well. We demonstrate that MAPS with PS is extremely accurate for solving general elliptic equations.
C.S. Chen 教授现为美国南密西西比大学数学系教授，是教育部和国家外国专家局“海外名师”项目外方合作者。C.S. Chen教授1979获台湾国立成功大学理学学士学位，1982年获美国南密西西西比大学理学硕士学位，1988年获路易斯安那大学拉斐特分校理学博士学位。C.S. Chen教授研究领域为无网格配置法、径向基函数以及边界元法等，学术成果丰硕，出版了4本专著和90多篇杂志论文。目前还担任Advances in Applied Mathematics and Mechanics 、Engineering Analysis with Boundary Elements，Journal of Mathematics and Applications， Journal of Computational methods以及Science & Military 等杂志的编辑。