报告人：刘进贤 教授 （台湾大学/河海大学）
报告摘要：A satisfactory choice of the sources in the method of fundamental solutions (MFS) is an important issue, because it is intimately related to the stability and accuracy of the MFS. In this talk we derive an energy merit functional and a simple merit functional to determine the optimal source points in the MFS, by solving the corresponding minimization problems. While the first is a quadratic nonlinear functional, the second is a linear functional. The new methods can improve the accuracy of the MFS in the solution of the Cauchy problem of the Laplace equation in an arbitrary bounded domain. The numerical test confirms that the optimal sources in the MFS can be determined fast and the accuracy of numerical solution is improved significantly.