We introduce and demonstrate the power of a method to speed up current iterative techniques for N-body modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the calculation of the fifth force becomes less accurate, but substantially faster, in high-density regions where it is weak due to screening. We focus on the nDGP model which employs Vainshtein screening, and test our method by running AMR simulations in which the solutions on the finer levels of the mesh (high density) are not obtained iteratively, but instead interpolated from coarser levels. We show that the impact this has on the matter power spectrum is below $1%$ for $k < 5h/{rm Mpc}$ at $z = 0$, and even smaller at higher redshift. The impact on halo properties is also small ($lesssim 3%$ for abundance, profiles, mass; and $lesssim 0.05%$ for positions and velocities). The method can boost the performance of modified gravity simulations by more than a factor of 10, which allows them to be pushed to resolution levels that were previously hard to achieve.
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