A staircase-approximation time-domain matrix integral equation approach to the computation of one-dimensional transient propagation through an inhomogeneous slab

A novel method, based on the staircase-approximation time-domain matrix integral equation (SATDMIE), is proposed to solve 1D transient propagation through an inhomogeneous slab. A numerical scheme is developed to compute the transient response iteratively. This scheme only needs to factorize a K by K matrix once, and requires O(NK/sup 2/) storage and matrix element computations. Here N and K are the number of time steps and spatial divisions, respectively. The whole theory framework is quite general. It can be extended to solve 3D problems like the transient radiation and scattering of wire antennas.