Solving numerical difficulties for element-free Galerkin analyses

This study solves the numerical problems associated with the element-free Galerkin method (EFGM) to perform analyses efficiently in shared-memory computers. The truncation error is generally large for the moving least-squares approximation, and this can be overcome by using orthogonal basis functions, 16-byte floats, or the local origin. Then, the analysis accuracy is similar to that obtained with the reproducing kernel particle approximation. Determining the index array of the global stiffness matrix requires a large amount of computer memory. We thus propose a scheme to overcome this problem using slightly more computer time but much less computer memory. A binary search is also proposed to find the support domain nodes for Gaussian points, and this method is much more efficient than the linear search one. A Fortran module is developed to establish parallel solutions in the EFGM, and the programmer does not need to handle the global stiffness directly.