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MADLens produces non-Gaussian cosmic shear maps at arbitrary source redshifts. A MADLens simulation with only 256^3 particles produces convergence maps whose power agree with theoretical lensing power spectra up to scales of L=10000. The code is based on a highly parallelizable particle-mesh algorithm and employs a sub-evolution scheme in the lensing projection and a machine-learning inspired sharpening step to achieve these high accuracies.