Because of its complex structure the parametrized fixed point action can not be simulated with the available local updating algorithms. We constructed, coded, and tested an updating procedure with $2+1$ light flavors, where the targeted $s$ quark mass is at its physical value while the $u$ and $d$ quarks should produce pions lighter than 300 MeV. In the algorithm a partially global gauge update is followed by several accept/reject steps, where parts of the determinant are switched on gradually in the order of their costs. The trial configuration that is offered in the last, most expensive, stochastic accept/reject step differs from the original configuration by a Metropolis $+$ over-relaxation gauge update over a subvolume of $\sim (1.3\mathrm{fm}{)}^4$. The acceptance rate in this accept/reject step is $\sim 0.4$. The code is optimized on different architectures and is running on lattices with $L_s\approx 1.2\mathrm{fm}$ and 1.8 fm at a resolution of $a\approx 0.15\mathrm{fm}$.

• Received 14 October 2005

DOI:https://doi.org/10.1103/PhysRevD.72.114508