Grid-based calculations of redshift-space matter fluctuations from
  perturbation theory: UV sensitivity and convergence at the field level
  Perturbation theory (PT) has been used to interpret the observed nonlinear
large-scale structure statistics at the quasi-linear regime. To facilitate the
PT-based analysis, we have presented the GridSPT algorithm, a grid-based method
to compute the nonlinear density and velocity fields in standard perturbation
theory (SPT) from a given linear power spectrum. Here, we further put forward
the approach by taking the redshift-space distortions into account. With the
new implementation, we have, for the first time, generated the redshift-space
density field to the fifth order and computed the next-to-next-to-leading order
(2 loop) power spectrum and the next-to-leading order (1 loop) bispectrum of
matter clustering in redshift space. By comparing the result with corresponding
analytical SPT calculation and $N$-body simulations, we find that the SPT
calculation (A) suffers much more from the UV sensitivity due to the
higher-derivative operators and (B) deviates from the $N$-body results from the
Fourier wavenumber smaller than real space $k_{\rm max}$. Finally, we have
shown that while Pad\'e approximation removes spurious features in morphology,
it does not improve the modeling of power spectrum and bispectrum.
