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An accelerated predictor-corrector scheme is presented to speed up thesimulation of 3D fatigue crack growth for problems with linear-elastic materialbehavior. Based on the highly accurate stress field - computed with the 3D dualboundary element method (Dual BEM) - the stress intensity factors (SIFs) arecalculated by an extrapolation method. The crack deflection as well as the crackextension is controlled by these SIFs. Due to the nonlinear behavior of crack growth anincremental procedure has to be applied. Based on experimental evidence it is assumedthat the crack front shape ensures a constant energy release rate along the whole crackfront, which means a constant KV. Starting from a crack front satisfying thisrequirement a predictor step is performed. Usually, the new determined crack frontdoes not fulfill the requirement of a constant energy release rate. Several correctorsteps are needed to find the correct crack front. Increasing the efficiency of thecorrector steps, the history of the crack path is taken into account in the predictorcorrectorscheme. Since the total number of simulations decreases the calculation timeis reduced significantly. The efficiency of the presented predictor-corrector scheme isdemonstrated by comparing numerical examples with precise experimental results.