Discreteness noise versus force errors in N-body simulations
We have investigated the effect of the numerical error of the force calculation on the accuracy of the result of collisionless N-body simulations. Our main result is that force calculation with a low accuracy — a few percent for each particle pair — is sufficient, irrespective of the number of particles. Higher accuracy is useless since the discreteness noise, i.e., the two-body relaxation effect, dominates the error. We have performed numerical experiments for two different cases: a special-purpose machine with low-precision hardware and the tree-code. In both cases, the two-body relaxation effect dominates the error and the effect of the error in the force calculation is practically negligible for all cases we tried.
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