Conservative Grids Used for the Two-Dimensional Electromagnetic Analysis

Abstract

Equivalent circuits of an elementary space cell that consist of lumped elements are proposed for constructing conservative grids used in the two-dimensional analysis of structures with arbitrary distributed permittivity and permeability. The derivation of the values of lumped elements is carried out on the basis of the finite-difference form of Maxwell's equations. In this case, all values of the obtained lumped capacitances and inductances take positive values, ensuring the computational stability and causality of the algorithms. It is demonstrated that the algorithms based on the grids obtained are numerically stable for positive, negative, and zero values of permittivity and permeability. When the values of the dielectric constant are lower than the dielectric constant of vacuum, including negative ones and equal to zero, the frequency dispersion in the proposed grid corresponds to the plasma model without taking into account the motion of positive ions and collisions, which makes it possible to use this model for the numerical electrodynamic analysis of an inhomogeneous plasma.