Three-dimensional improved XFEM (IXFEM) for static crack problems

An improved XFEM (IXFEM) for three-dimensional linear elastic fracture mechanics (LEFM) problems is developed. It utilizes an extra-dof free PU approximation to fundamentally overcome the linear dependence and the ill-conditioning issues of the standard XFEM and the Corrected XFEM (CXFEM). The introduced PU approximation is based on local least-squares fitting with a one-point interpolation constraint. The resulting PU approximation interpolates and has no difficulties in boundary treatments. Detailed comparisons are made with the current XFEMs in 3D in terms of accuracy, convergence, and conditioning properties or solver efficiency. Better accuracy and convergence are demonstrated. The remarkably better efficiency with a subspace iterative solver, the de-facto in large-scale simulation, is observed—the number of iterations for the system of linear equations is reduced by orders of magnitude compared with the current XFEMs.