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The N2 computations implicit in the Coulomb and other long range interactions remain the critical bottleneck in atomic-level simulations of the structure and dynamics of large systems. We report here the cell multipole method which scales linearly with N and requires only modest memory. To demonstrate the feasibility of this approach, we report systematic calculations on realistic polymer systems with up to 1.2 million atoms on a laboratory workstation. The method becomes faster than the exactdoi:10.1063/1.463935 fatcat:jlo44qr2sbd6fdvmuvatys34xq