Accurate cosmological simulations that include the effect of non-linear matter clustering as well as of massive neutrinos are essential for measuring the neutrino mass scale from upcoming galaxy surveys .
Typically , Newtonian simulations are employed and the neutrino distribution is sampled with a large number of particles in order to beat down the shot noise .
Here we perform very efficient simulations with light massive neutrinos which require virtually no extra cost over matter-only simulations , and furthermore do not require tracer particles for the neutrinos .
Instead , we use a weak-field dictionary based on the recently developed Newtonion motion approach , where Newtonian simulations for matter are paired with a linear relativistic Boltzmann code to allow for an absorption of the neutrino evolution into a time-dependent coordinate transformation .
For this , only minimal modifications in existing N-body codes are required , which we have explicitly implemented in gevolution and gadget-2 .
Our fast method determines the non-linear matter power spectrum to permille-level precision when compared against state-of-the-art simulations that have been performed for 0.1 { eV } \leq \sum m _ { \nu } \leq 0.3 eV .