An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique

Simulations of GPR in dispersive media using a frequency-dependent PSTD algorithm

“…In contrast to the previous observations, in [16]- [18] it was shown that by a proper integration the RC approach can be made nearly as accurate as the PLRC approach.…”

“…Here we adopt the slightly improved RC and PLRC approaches [16], [17]. It was recently found [16]- [18] that, unlike the previous results, the RC approach can be made accurate despite its piecewise constant approximation within each time step.…”

“…This dispersion is mainly caused by the presence of moisture in the soil. A common model for soil is the Debye medium whose susceptibility function is given by (18) where is the relative static permittivity, is the Debye relaxation time constant, and is the pole amplitude. The Debye medium can be considered a special case of the general equation (5) with (19) Therefore, given (19) for an arbitrary Debye medium, (12) and (13) can be solved efficiently without the expensive temporal convolution.…”

“…Traditionally, this is accomplished by the FDTD method [1]- [18] through an Yee grid [19]. In the PSTD algorithm [20]- [22], instead of using a conventional Yee grid, we use a centered grid where all field components and material properties are located at the center of the unit cell of size…”

“…The finite-difference time-domain (FDTD) method [19] has been widely used together with the above approaches to simulate transient electromagnetic fields in dispersive media [1]- [18]. These frequency-dependent FDTD methods use the finite differences to approximate the spatial and temporal derivatives.…”