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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., 18 pages, 7 figures, accepted for publication in PRD

International audience; This paper tests the performance of coupling coefficients of a Dirichlet–Robin transmission procedure in the context of steady conjugate heat transfer (CHT). Particular emphasis is put on the optimal coefficients highlighted recently in a theoretical study based on a normal mode stability analysis. This work can be seen as the logical continuation of that study in order to assess the relevance of the coefficients provided by the model problem in a realistic aerothermal computation. First, the numerical and physical CHT modeling methodologies are presented. Then, the optimal procedure applied to a Dirichlet–Robin algorithm (one-coefficient method) is briefly described. In order to gauge the ability of this model to predict the stability and convergence properties of a realistic case, it is compared on a heated cylinder in a flowfield test case. A series of five coupling coefficients and three Fourier numbers are considered. These parameters are introduced into the model problem as data to compute the amplification factor and the stability limits. The stability and convergence properties predicted by the model problem are then compared to those obtained in the CHT computation. This comparison shows an excellent overall agreement. Moreover, for all the Fourier numbers considered, the numerical solution is stable and oscillation-free when the optimal coefficient of the model problem is used. This would suggest that the one-dimensional normal mode analysis can provide relevant coefficients directly applicable to real CHT problems.