  Gravitational wave (GW) astronomy offers the potential to probe the
wave-optics regime of gravitational lensing. Wave optics (WO) effects are
relevant at low frequencies, when the wavelength is comparable to the
characteristic lensing time delay multiplied by the speed of light, and are
thus often negligible for electromagnetic signals. Accurate predictions require
computing the conditionally convergent diffraction integral, which involves
highly oscillatory integrands and is numerically difficult. We develop and
implement several methods to compute lensing predictions in the WO regime valid
for general gravitational lenses. First, we derive approximations for high and
low frequencies, obtaining explicit expressions for several analytic lens
models. Next, we discuss two numerical methods suitable in the intermediate
frequency range: 1) Regularized contour flow yields accurate answers in a
fraction of a second for a broad range of frequencies. 2) Complex deformation
is slower, but requires no knowledge of solutions to the geometric lens
equation. Both methods are independent and complement each other. We verify
sub-percent accuracy for several lens models, which should be sufficient for
applications to GW astronomy in the near future. Apart from modelling lensed
GWs, our method will also be applicable to the study of plasma lensing of radio
waves and tests of gravity.
