Global-Local-Integration-based Kernel Approximation Methods

Time: 2016-09-29 23:15:00

Topic： Global-Local-Integration-based Kernel Approximation Methods

Speaker： Benny Y. C. HON, City University of Hong Kong 

Abstract：In this talk, the recent development in global, local, and integration-based meshless computational methods via the use of kernels will be presented. The local kernel approximation method is an extension to solve large scale problems which has hindered the practical application of the global method for years due to the ill-conditioning of the resultant full coefficient matrix. Because of the intrinsic stable and accurate advantages of numerical integration and spectral convergence of kernels approximation, the kernel-based methods can solve multi-dimensional boundary value problems (BVPs) under irregular domain with certain kinds of stiffness. The main idea of the integration-based method is to transform the original partial differential equation into an equivalent integral equation whose approximation can be sought by standard numerical integration techniques. Unlike the use of finite quotient formula in the classical finite difference method (FDM), the integration-based method uses numerical quadrature formula to approximate the unknown solution and its derivatives and hence avoids the well-known optimal round off-discretization trade off error in FDM. The integration-based method has recently applied to solve inverse heat conduction problem. Numerical examples in 2D will be given to verify the efficiency and effectiveness of the proposed methods.

Time： 2016-09-29 10:30--11:30 a.m.
Location：School of Mathematical Sciences