An Eigencurrent Approach to the Analysis of Electrically Large 3-D Structures Using Linear Embedding via Green's Operators

Abstract

We present an extension of the linear embedding via Green's operators (LEGO) procedure for efficiently dealing with 3-D electromagnetic composite structures. In LEGO's notion, we enclose the objects forming a structure within arbitrarily shaped domains (bricks), which (by invoking the equivalence principle) we characterize through scattering operators. In the 2-D instance, we then combined the bricks numerically, in a cascade of successive embedding steps, to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects. In the 3-D case, however, this process becomes quite soon impracticable, in that the resulting scattering matrices are too big to be stored and handled on most computers. To circumvent this hurdle, we propose a novel formulation of the electromagnetic problem based on an integral equation involving the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">total inverse scattering operator</i> of the structure, which can be written analytically in terms of scattering operators of the bricks and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transfer operators</i> among them. We then solve this equation by the method of moments combined with the eigencurrent expansion method, which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures.