A Fast Solver for 3D Meshless Analysis Based on RPIM

Abstract

Mshless method is an effective tool for solving partial differential equations. In this method, CPU-time is wasted mainly in calculating shape functions. The modified radial point interpolation method (RPIM) has been proposed for yielding fast computation. In the radial point interpolation based methods, the shape functions can be evaluated by solving the linear systems and the key of the fast computation is to create the matrices of the linear systems in advance of the shape function evaluations. The purpose of this study is to solve three-dimensional Poisson problems using the modified RPIM, which requires less CPU-time than the RPIM.