Venue: Local Kernel-Based Approximation Method for solving Inverse and Large Scale Problems

Speaker: Dr. Benny Hon

Time:  3 March 2012,10:00-11:00

Location: Room 201, Sir Run Run Shaw Business Adminisration Building, Yuquan Campus

Abstract: In this talk we present the development of meshless computational method based on the use of kernel-based functions for solving various physical problems.   Properties of some special kernels such as radial basis functions; harmonic kernels; fundamental and particular solutions; and Green’s functions will be discussed.   For tackling the well known ill-conditioned resultant system of equations, the method has recently been localized so that application to large scale engineering and industrial problems is now feasible. The method requires only a set of nodes in the domain and on the boundary from which all governing equations are solved in strong formulation without the need of tedious integrations. The refinement and redistribution of the nodes in adaption to moving boundary or rapid changing gradients in field variables can efficiently be made.   The method is proven to be efficient; accurate; and easy to code. For solving inverse (and hence ill-posed) problems, we will present the recent successful combination of the kernel-based approximation method with fundamental solutions; Laplace transform and Tikhonov regularization techniques to solve some inverse problems such as Cauchy and backward problems of Time-Fractional Order Partial Differential Equations.