Fast generation of macro basis functions for LEGO through the adaptive cross approximation

We present a method for the fast generation of macro basis functions in the context of the linear embedding via Green´s operators approach (LEGO) which is a domain decomposition technique based on the combination of electromagnetic bricks in turn described by means of scattering operators. We show that, when the scattering operators are rank-deficient, a reduced set of macro basis functions defined on the surface of the bricks can be obtained through the adaptive cross approximation of the scattering operator.