The performances of different methods used for the computation of the gradient of the free space Green's function for doubly periodic infinite arrays are investigated, for spacings smaller than the wavelength. An optimal transition between plane wave and cylindrical wave decompositions is proposed and an extension of the method is proposed for the large wavelength case. The joint use of different wave decompositions, combined with the Levin accelerator, allows to obtain exponential convergence for all observation points.
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Guérin et al. (2009) studied this question.
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