A New Variation of Point Collocation: The Meshless Finite Mixture (MFM) Method

Abstract

In this paper, a new variation of point collocation with finite mixture approximation, the meshless finite mixture (MFM) method, is developed. Based on the finite mixture theorem, the method can consist of two or more existing meshless techniques so as to exploit their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this instance, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. For higher numerical accuracy and stability, the least-square approach is then employed to optimize the weighting coefficients in the construction of the approximation. To validate the presently developed MFM method, several 2-D numerical studies are carried out. The numerical results clearly indicate that the optimal weighting coefficients deployed in the MFM method enhance the numerical accuracy and stability, for various PDBV problems.