A comparison of two types of macro basis functions defined on LEGO electromagnetic bricks

Linear embedding via Green´s operators (LEGO) is a domain decomposition method that uses electromagnetic “bricks” to solve wave scattering problems. The algebraic form of the relevant functional equations (which are derived by invoking the surface equivalence principle) is a linear system characterized by a full and possibly large matrix. The size of the system can be effectively reduced by adopting macro basis functions defined on the surface of a brick through 1) the eigencurrents expansion method (EEM) and 2) the Adaptive Cross Approximation (ACA). The two methods lead to the same results, though the ACA macro basis functions are faster to compute.