On the convergence of the eigencurrent expansion method applied to Linear Embedding via Green's Operators (LEGO)

The scattering from a large complex structure comprised of many objects may be efficiently tackled by embedding each object within a bounded domain (brick) which is described through a scattering operator. Upon electromagnetically combining the scattering operators we arrive at an equation which involves the total inverse scattering operator S-1 of the structure: We call this procedure linear embedding via Green's operators (LEGO). To solve the relevant equation we then employ the eigencurrent expansion method (EEM)-essentially the method of moments with a set of basis and test functions that are approximations to the eigenfunctions of S-1 (termed eigencurrents). We have investigated the convergence of the EEM applied to LEGO in cases when all the bricks are identical. Our findings lead us to formulate a simple and practical criterion for controlling the error of the computed solution a priori.