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Summary form only given. Spectral methods and mode matching techniques are well established methods to solve waveguide and scattering problems. Many rigorous methods exist but large efforts remain to be made in obtaining 3D electromagnetic codes that are sufficiently robust and fast. The coupled-wave method also called the Fourier modal method (FMM) is an example of the most efficient and commonly used method to solve diffraction problems. This choice is known to lead to slow convergence in the case of large index contrast or when the index profile variation is very localized. Subwavelength slits arrays in metallic films are typical examples of such a situation. Hence, we can explore if other expansions would be more efficient. On the one hand, in the field of signal processing, functions with a compact support showed a very strong potential through their ability to provide fast convergence. On the other hand, within the framework of spectral methods, The Finite Difference Modal Method is one such attempt. It can be considered as a spectral method in which the field is expanded into pulse functions. Our idea is to employ more elaborate compact basis functions in order to improve the convergence speed. Following the pioneering work of Edee et al, we use the splines as a basis functions. These functions are reputed to provide faster convergence and encouraging results have already been obtained in several papers. It is well known that concept of adaptive spatial resolution or non uniform sampling scheme increases the convergence speed. Extrapolating them to our method, we obtain even more accurate results with less computational effort.