Kernel Based Meshless Method: Kernel Based Meshless Method for Solving Ill-posed and High-dimensional Problems

In the past decades, the development of meshless methods has become a very active research area. There are basically two types of meshless methods: weak formulation and strong collocation. The weak formulation meshless methods include those novel methods such as Element-free Galerkin method(EFG), smoothed particle hydrodynamics(SPH), reproducing kernel particle method(RKPM), Smoothing Finite Element Method(SFEM) and Meshless local Petrov Galerkin(MLPG). The strong collocation methods began with the so-called radial basis functions(RBFs) method first developed by Kansa and other collocation-type meshless methods such as boundary knot method, finite point method and the method of fundamental solutions(MFS). These newly established meshless methods have been successfully developed and applied to solve many real-life problems in science and engineering.