Convergence and Efficiency of Different Methods to Compute the Diffraction Integral for Gravitational Lensing of Gravitational Waves

TL;DR

This paper evaluates various numerical methods for computing the diffraction integral in gravitational wave lensing, introduces a new combined approach, and demonstrates its improved accuracy and efficiency for analyzing lensed GW waveforms.

Contribution

It introduces a novel combined numerical method that enhances the accuracy and efficiency of diffraction integral calculations in gravitational wave lensing.

Findings

The combined method outperforms existing techniques in accuracy.

The new approach reduces computation time significantly.

It provides reliable results for lensed gravitational waveforms.

Abstract

Wave optics may need to be considered when studying the lensed waveforms of gravitational waves (GWs). However, the computation of the diffraction integral (amplification factor) in wave optics is challenging and time-consuming. It is vital to develop an accurate and efficient method to calculate the amplification factor for detecting lensed GW systems. In this paper, we investigate the convergence of the diffraction integral for gravitational lensing of GWs and analyze the accuracy and efficiency of a number of numerical methods that can be used to calculate this integral, including the integral mean method, asymptotic expansion method, Levin's method, zero points integral method, etc. We further introduce a new method by combining the zero points integral and the asymptotic expansion methods to calculate the diffraction integral, which provides an efficient and accurate way to calculate the lensed waveform of GWs.