Error analysis of the moving least square material point method for large deformation problems

The moving least squares material point method (MLS-MPM) is widely used in large deformation problems and computer graphics, yet its error analysis remains challenging due to multiple error sources. We analyze moving least squares approximation errors, single-point integration errors, computation errors of physical quantities, and stability. The key to the analysis is deriving the single-point integration error for moving least squares shape functions. The main results demonstrate a significant correlation between error estimates and parameters such as node spacing, particle width, and particle density per cell. Numerical experiments further demonstrate that higher-order shape functions, constructed by combining basis functions with Gaussian, cubic spline, and quartic spline functions, significantly reduce errors, improving computational accuracy and reliability.