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报告人：Benny Hon
Department of Mathematics
City University of Hong Kong

摘要：
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; Green’s 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.