Analysis of nonlinear problems in electrodynamics by means of surface impedance boundary conditions (SIBC) combined with transfer matrix method

Surface Impedance Boundary Conditions applied to solving nonlinear electrodynamic systems

“…Therefore, the procedures for determining Z c and computing field distribution need to be interrelated. A transfer matrix method based concept for numerical procedure to compute surface impedance was presented elsewhere [10,11]. Further in this chapter a brief summary of it, completed with some significant supplements is provided.…”

“…Due to continuity conditions for the tangent components of the electric and magnetic fields, E and H, respectively at the boundary between the sectors k and k + 1, it can be shown that [10,11] …”

“…By neglecting within the n + 1 area the wave incident onto the coordinate s 3 , then with (32) and (39) it is obtained [11]: According to the description provided above the procedure for computing Z c comes down to computing the P matrix, which is a simple product of 2 nd rank matrices (see formula (39)). Still, for nonlinear cases M k matrix elements cannot be directly computed, as it is necessary to know local magnetic permeability μ k values, which are dependent on the magnetic field distribution to be computed.…”

“…Therefore, the concerned procedure has to be linked with another procedure (e.g. FEM, BEM, FSM -see [8,9,11]) for computing the electromagnetic field distribution within the dielectric area under the SIBC condition set at the boundary surfaces. Such a concept as well as the results of introductory numerical tests were reported elsewhere [8,9,11].…”

“…FEM, BEM, FSM -see [8,9,11]) for computing the electromagnetic field distribution within the dielectric area under the SIBC condition set at the boundary surfaces. Such a concept as well as the results of introductory numerical tests were reported elsewhere [8,9,11]. It consists in iterative finding electromagnetic field distribution that is self-consistent with the surface impedance distribution at the conducting sectors surfaces of the considered system.…”