Nyquist-resolving gravitational waves via orbital frequency-based refinement

TL;DR

This paper introduces ORBIT, a dynamic grid refinement method based on orbital frequency, which improves gravitational waveform accuracy and computational efficiency in numerical relativity simulations.

Contribution

The paper presents a novel in situ refinement criterion using orbital frequency to optimize grid resolution for gravitational wave simulations.

Findings

Decreases waveform noise by an order of magnitude.

Better resolves high-order wave amplitudes through merger.

Reduces computational cost by a factor of four.

Abstract

Adaptive mesh refinement efficiently facilitates the computation of gravitational waveforms in numerical relativity. However, determining precisely when, where, and to what extent to refine when solving the Einstein equations poses challenges; several ad hoc refinement criteria have been explored in the literature. This work introduces an optimized resolution baseline derived in situ from the inspiral trajectory (ORBIT). This method uses the binary's orbital frequency as a proxy for anticipated gravitational waves to dynamically refine the grid, satisfying the Nyquist frequency requirements on grid resolution up to a specified spin weighted spherical harmonic order. ORBIT sustains propagation of gravitational waves while avoiding the more costly alternative of maintaining high resolution across an entire simulation, both spatially and temporally. We find that enabling ORBIT decreases waveform noise by an order of magnitude and better resolves high-order wave amplitudes through merger. Combined with WAMR and other improvements, updates to Dendro-GR decrease waveform noise, decrease constraint violations, and boost refinement efficiency each by factors of $\mathcal{O}(100)$, while reducing computational cost by a factor of four. ORBIT and other recent improvements to Dendro-GR begin to prepare us for gravitational wave science with next-generation detectors.