  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.
