| 报告题目： | Kernel-based Approximation Methods for Ill-posed Problems |
| 报 告 人： | Benny Hon |
| 香港城市大学数学系 | |
| 报告时间： | 4月18号下午14:00-15:00 |
| 报告地点： | 数学系九龙湖第一报告厅 |
| 相关介绍： | In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Greens functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Tikhonov regularization technique to solve Cauchy problems and inverse heat conduction/source identification problems will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The L-curve method for searching an optimal regularization parameter is then adopt to obtain stable solution from measured data with noises. |
