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Wave optics may need to be considered when studying the lensed waveforms ofgravitational waves (GWs). However, the computation of the diffraction integral(amplification factor) in wave optics is challenging and time-consuming. It isvital to develop an accurate and efficient method to calculate theamplification factor for detecting lensed GW systems. In this paper, weinvestigate the convergence of the diffraction integral for gravitationallensing of GWs and analyze the accuracy and efficiency of a number of numericalmethods that can be used to calculate this integral, including the integralmean method, asymptotic expansion method, Levin's method, zero points integralmethod, etc. We further introduce a new method by combining the zero pointsintegral and the asymptotic expansion methods to calculate the diffractionintegral, which provides an efficient and accurate way to calculate the lensedwaveform of GWs.

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