Interpolating compact binary waveforms using the singular value decomposition

TL;DR

This paper introduces a singular value decomposition-based interpolation method for efficiently modeling gravitational waveforms from compact binary mergers, reducing computational costs in waveform generation.

Contribution

It presents a novel numerical interpolation scheme using SVD to construct waveforms across parameter space from limited simulations.

Findings

Effective interpolation within parameter space

Potential for faster waveform generation

Applicability to parameter estimation

Abstract

Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to model the gravitational waveform of the merger epoch of compact binary coalescence, the full Einstein equations must be solved numerically for the entire mass and spin parameter space. However, this is computationally expensive. Several models have been proposed to interpolate the results of numerical relativity simulations. In this paper we propose a numerical interpolation scheme that stems from the singular value decomposition. This algorithm shows promise in allowing one to construct arbitrary waveforms within a certain parameter space given a sufficient density of numerical simulations covering the same parameter space. We also investigate how similar approaches could be used to interpolate waveforms in the context of parameter estimation.