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Perturbation theory (PT) has been used to interpret the observed nonlinearlarge-scale structure statistics at the quasi-linear regime. To facilitate thePT-based analysis, we have presented the GridSPT algorithm, a grid-based methodto compute the nonlinear density and velocity fields in standard perturbationtheory (SPT) from a given linear power spectrum. Here, we further put forwardthe approach by taking the redshift-space distortions into account. With thenew implementation, we have, for the first time, generated the redshift-spacedensity 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 ofmatter clustering in redshift space. By comparing the result with correspondinganalytical SPT calculation and $N$-body simulations, we find that the SPTcalculation (A) suffers much more from the UV sensitivity due to thehigher-derivative operators and (B) deviates from the $N$-body results from theFourier wavenumber smaller than real space $k_{\rm max}$. Finally, we haveshown that while Pad\'e approximation removes spurious features in morphology,it does not improve the modeling of power spectrum and bispectrum.

Grid-based calculations of redshift-space matter fluctuations from perturbation theory: UV sensitivity and convergence at the field level