Local Radial Basis Function Method for Solving Non-local Diffusion Problems

来源:力学与工程学院  返回:ca88     日期:2019/7/10 9:31:30   点击数:2019  

时间:2019-07-15 10:00


报告人:Benny Y.C. HON



Prof. Benny Hon’s major research interests include meshless computation using radial basis functions for solving various types of partial differential equations and numerical methods for solving inverse problems based on fundamental solutions and reproducing kernels. He is particularly keen in promoting the meshless radial basis functions method for simulations of tides and waves; multiphasic fluid flows; micro-electro-mechanical systems; inverse heat conduction and image reconstruction. He is now serving as an Associate Editor for the Journal of Inverse Problems in Science and Engineering and member on the editorial board for seven international journals including the journal of Advances in Computational Mathematics and Engineering Analysis with Boundary Elements with recent emphasis on meshless and mesh reduction methods. He has also co-edited several special issues on meshless computations and inverse problems for the journal of Computers and Mathematics with Applications and Advances in Computational Mathematics.


In this talk, the recent development in global, local and integration-based meshless computational methods via the use of radial basis functions (RBF) will be presented. In particular, the local radial basis function computational method (LRBFCM) is an extension to solve large scale problems which has hindered the practical application of the global RBF method for years due to the ill-conditioning of the resultant full coefficient matrix. The LRBFCM has recently been applied to solve cavity flows problems with free surface and some non-local diffusion problems. Because of the meshless and accurate advantages of RBF approximation, the LRBFCM can solve multi-dimensional boundary value problems under irregular domain with various kinds of stiffness. Numerical examples in 2D will be given to verify the efficiency and effectiveness of the proposed methods.



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