Application of layered medium Green's function in low frequency models for numerical solutions

An accurate and efficient technique is presented for obtaining numerical solutions of microstrip structures at low frequencies. In this approach, a new form of the electric-field spatial-domain Green's function is used in a symmetrical form that simplifies the discretization of the integral equation using the method of moments (MoM). Hence, a Helmholtz decomposition of the unknown currents is achieved by applying the loop-tree decomposition of the currents. However, the MoM matrix thus obtained still cannot be solved efficiently by iterative solvers due to the large number of iterations required. Consequently, a permutation of the loop-tree currents by a connection matrix is proposed to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers.