Optimization of a stabilized X-FEM formulation for frictional cracks

An efficient stabilized nonlinear LATIN solver dedicated to frictional cracks in the X-FEM framework is proposed. The performance of such a solver has already been emphasized in detail in a previous paper of Gravouil et al. [Stabilized global–local X-FEM for 3D non-planar frictional crack using relevant meshes, Int. J. Numer. Methods Eng. 88 (2011)1449–1475] Here, an optimization of the search direction of the LATIN solver is proposed. Intrinsic a priori formulas are proposed independently on the friction coefficient, the finite element mesh, the geometry and the boundary conditions. About one hundred thousand of calculations have been carried out in order to show the existence of a unique set of parameters ensuring the optimal convergence rate. The number of iterations required to reach the given level of accuracy is plotted versus two numerical parameters introduced, the search direction k and the stabilization operator ξ . A considerable decrease in the number of iterations and thus in the computing time is obtained, an important condition to carry out with a maximum efficiency of 3D simulations.