报告题目：Homotopy method of fundamental solutions for solving certain nonlinear
partial differential equations
报 告 人：蔡加正(Chia-Cheng Tsai)博士
高雄海洋科技大學海洋環境工程系教授、成功大學國際波動力學中心研究教授
报告时间：2016年01月21日（周四）下午14:00-16:00
报告地点：江宁乐学楼（1105室）
主办单位：力学与材料学院
报告摘要：
In thistalk,we will presentthe homotopymethod of fundamental solutions (HMFS)to solve certain nonlinear partial differential equations (PDE).In the HMFS, the homotopyanalysis method (HAM)is combined with the method of fundamental solutions (MFS) and themethod of particular solutions (MPS), which is based on theaugmented polyharmonic spline (APS)of high orders.TheMFS-MPS is a very accurate meshless numerical method which is capable of solving inhomogeneous PDEs if the fundamental solution and the analytical particular solutions of the APS associated with the considered operator are known. In the solution procedure,the HAM is applied to convert the considered nonlinear PDEs into a sequence of linear inhomogeneous PDEs, which can be solved by theMFS-MPS. In order to solvestrongly nonlinear problems, two auxiliary parameters are introduced to ensure the convergence of the HAM. Therefore, theHMFScan be applied to solve problems of strongly nonlinear PDEs, including even those whose governing equation and boundary conditions do not contain any linear terms. Therefore, it can greatly enlarge the application areas of the MFS. Several numerical experiments were carried out to validate the proposed method.