Lower hybrid (LH) waves are very important for heating and current drive in tokamaks. Phased arrays of rectangular waveguides, generally called grills, are typically used as launchers. We develop a code which solves, in the 3D geometry of the grill structure, the problem of efficient coupling: the power density spectrum of the emitted waves, the power reflection coefficient, the power lost by the waves launched in the inaccessible region and the directivity of the waves transmitted into the accessible region. The code is also able to determine the 3D electric field in front of the grill. An efficient adaptive full wave solver is used to determine the wave propagation in a 1D plasma slab geometry. To evaluate the very large number of 2D k-space infinite integrals for the coupling elements, we have developed a method based on high order Gaussian quadratures combined with 2D B-splines in the accessible region for the plasma related part of the integrands. This method is well suited to handle large structures and many modes because the computational time is only weakly dependent on the size of the problem. An iterative evaluation of the integrands in the inaccessible region is adopted to handle the presently overlooked near singular behaviour of the integrands as well as the spectral power density associated with the eigenmodes. The role of collisions is clarified in this context. The code is applied to several COMPASS grills operating either at 1.3 GHz or at 3.7 GHz. First we thouroughly analyse the original 1.3 GHz, 8-waveguide conventional grill at various waveguide phasing. Then, the coupling of two grill designs for 3.7 GHz is solved. The suitability of all the grills is discussed, showing compatible grill and plasma parameter ranges.