A time domain element differential method for solving electromagnetic wave scattering and radiation problems

Abstract

In this paper, a simple and efficient numerical method named time domain element differential method (TD-EDM) is proposed to solve electromagnetic wave scattering and radiation problems. In the method, the governing equations as well as boundary conditions are directly solved in a strong-form formulation. The computational domain is discretized using isoparametric elements, and the spatial derivatives of basic variables appearing in the governing equations are calculated by a set of analytical expressions of partial derivatives of the element shape functions with respect to global coordinates, and time derivatives of the basic variable are computed using the Newmark time integration scheme. The absorbing boundary condition (ABC) is applied on the truncation boundary to absorb the outgoing waves, which realizes the numerical modeling of an open infinite region. The incident wave is induced in the total-field region by setting equivalent electromagnetic currents on the total-field/scattering-field (TF/SF) boundary. The TD-EDM equations at the nodes located near the total-field boundary are modified to satisfy the conditions that the electric field values of all nodes involved belong to either the total-field or the scattered field. The near-to-far-field transformation technique is used to calculate the far scattered field, and then the target's Radar Cross Section (RCS) is evaluated. Several numerical results including the radiation from a line current source and the target's Radar Cross Section (RCS) are given to validate correctness of the proposed method.