Finite-difference time-domain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils

Abstract

Abstract-

Finite element study of time‐dependent Maxwell's equations in dispersive media

“…Actually we only need τ = O(t 0 ), which is always satisfied in pactical applications (e.g. [17] and [18]). …”

Finite-difference computation of transient electromagnetic waves for cylindrical geometries in complex media

“…The analytical continuation of Maxwell's equations to a complex domain is a general setting to understand the PML concept, allowing it to be extended to various coordinate systems [38]- [40] and to more general media such as dispersive or (bi-)anisotropic [42], [43]. This analytical continuation can be viewed as giving additional degrees of freedom and to Maxwell's equations.…”

“…The intermediate steps in the derivation of the combined PML-PLRC-FDTD time-stepping scheme in cylindrical coordinates are analogous to the Cartesian case [43] and for brevity, will not be discussed here. The final equations for the PML-PLRC-FDTD time-stepping scheme for the electromagnetic fields in cylindrical coordinates are On the right-hand side of (33)- (35), the other pertinent quantities are updated as follows: (36) (37) (38) (39) where is replaced with , , or .…”

“…2 compares the results for the FDTD simulations in a dispersive half-space against this pseudo-analytical solution. The half space dispersion parameters are obtained by fitting a two-species ( 2) Debye model to the experimental data reported by Hipp [52] for the Puerto Rico type of clay loams (with 5% moisture content), which can be found in [43]. The domain is discretized using a ( ) (40,80,60) grid.…”

“…We extend the PML ABC to the cylindrical system using the complex coordinate stretching approach [28], [36], [38]- [43]. Two numerical schemes are developed in the time domain.…”