A localized Fourier collocation method for 2D and 3D elastic mechanics analysis: Theory and MATLAB code

Abstract

This paper documents the first attempt to apply the localized Fourier collocation method (LFCM), a recently published meshless collocation method, for solving 2D and 3D elastostatic problems. The approach first divides the entire domain into a series of intersecting sub-domains. Within each sub-domain, the unknown functions are approximated by utilizing the pseudo-spectral Fourier collocation technique. The method integrates the merits of the rapid convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique. This combination results in a novel framework that is highly suitable for large-scale and high-precision engineering simulations. Extensive numerical experiments, involving both 2D and 3D elastostatic problems, are presented to showcase the precision and efficiency of the current method. The source codes for numerical examples studied in this work are also provided.