A marching-on-in-degree solution of volume integral equations for transient electromagnetic scattering by bi-isotropic objects

A time-domain volume integral equation solved by the marching-on-in-degree scheme is presented for the analysis of transient electromagnetic scattering from three-dimensional inhomogeneous bi-isotropic objects. Based on the volume equivalence principle, the volume-based coupled integral equations for electric and magnetic flux densities are formulated. The transient variations of the electric and magnetic flux densities are expanded in terms of weighted Laguerre polynomials. With the use of the Galerkin spatial and temporal testing procedure, the proposed algorithm overcomes the late-time instability problem that often occurs in the marching-on-in-time approach. Numerical results are presented to illustrate the accuracy and versatility of the proposed algorithm.