Mathematical modeling of impedance for a perfect electric conductors system with lumped elements in a homogeneous medium using the augmented electric field integral equation

The solution of Maxwell's equations for perfect electric conductors in a homogeneous medium is considered using an augmented electric field integral equation (A-EFIE). The resulting system of equations is discretized using the Galerkin method. The method for constructing a numerical scheme is presented, which allows calculating the impedance of a printed circuit board power system together with the lumped electrical components placed on it. Additionally, boundary conditions typical for microelectronic devices are considered. The system of linear equations obtained through discretization is solved iteratively, with the fast multipole method used to accelerate the matrix-vector product. The methodology was verified using the example of scattering of a monochromatic wave by a sphere, for which an analytical solution exists, as well as through the impedance modeling of a printed circuit board, where the results were compared with those obtained from commercial software.