Space-time Hallen Integral Equation Research Articles

On deterministic-stochastic time domain study of dipole antenna for GPR applications

A deterministic-stochastic transient study of Ground Penetrating Radar (GPR) dipole antenna radiating in a presence of a two-media configuration is carried out in the paper. A deterministic direct time domain formulation is based on the corresponding space-time Hallen integral equation. The numerical solution is carried out via the improved space-time variant of the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). The Stochastic-Collocation (SC) method is then applied to determine accurate confidence intervals due to the random variations of GPR input parameters. Once obtaining the current along the dipole antenna, it is possible to calculate other parameters of interest for GPR dipole antenna behavior, such as the field reflected from the interface of two media, or the field transmitted into a lower half-space. Some illustrative numerical results for the transient current along the dipole antenna and transient electric field transmitted into the lower half-space are given.

Electromagnetic Field Coupling to Overhead Wire Configurations: Antenna Model versus Transmission Line Approach

The paper deals with two different approaches for the analysis of electromagnetic field coupling to finite length overhead wire: the wire antenna theory (AT) and the transmission line (TL) method. The analysis is carried out in the frequency and time domain, respectively. Within the frequency domain analysis the wire antenna formulation deals with the corresponding set of Pocklington integrodifferential equation, while the transmission line model uses the telegrapher's equations. The set of Pocklington equations is solved via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM), while the telegrapher’s equations are treated using the chain matrix method and the modal equation to derive per-unit-length parameters. For the case of the time domain analysis AT model uses the space-time Hallen integral equation set, while TL approach deals with the time domain version of the telegrapher’s equations. Hallen equations are handled via time domain version of GB-IBEM, while time domain telegrapher’s equations are solved by using Finite Difference Time Domain (FDTD) method. Many illustrative computational examples for the frequency and time domain response, respectively, for several configurations of overhead wires, obtained via different approaches, are given in this paper.

Time domain modelling of thin wire arrays in the presence of a two media configuration using the boundary element analysis

Transient response of a multiple wire configuration in the presence of a two-media configuration excited by a voltage source (antenna mode) or illuminated by an incident field is analysed using the boundary element method (BEM). The analysis is based on the solution of the corresponding set of the coupled space-time Hallen integral equation and it is carried out directly in the time domain. The influence of a two media configuration is taken into account via the space time reflection coefficient. The corresponding integral equation set is handled via the time domain variant of the Galerkin–Bubnov indirect boundary element method (GB-IBEM). Some illustrative numerical results for both antenna and scattering mode are presented in the paper.

Time-Domain Modeling of Electromagnetic Field Coupling to Finite-Length Wires Embedded in a Dielectric Half-Space

The transient behavior of a single straight line embedded in a dielectric half-space and illuminated by the electromagnetic pulse (EMP) is analyzed directly in the time domain using the wire antenna approach. The formulation is based on the corresponding space-time Hallen integral equation. The effects of a two-media configuration are taken into account via the Fresnel reflection and transmission coefficient, respectively. The space-time Hallen integral equation is handled by the time-domain version of the indirect Galerkin-Bubnov boundary element method. The transient response obtained using the direct time-domain approach is compared with the results obtained via an indirect frequency-domain analysis method. Some illustrative numerical results are presented in the paper. Numerical results obtained via the different approaches agree satisfactorily, i.e., the maximum deviation between the results is around 6%.

Transient Response of Nonlinearly Loaded Wires in a Two Media Configuration

The transient behavior of thin wires with nonlinear resistive load in the presence of a dielectric half-space is analyzed directly in the time domain. The nonlinear wire problem is formulated by the space-time Hallen integral equation. The effect of a two-media configuration is taken into account via the space-time reflection coefficient appearing within the Green function. The resulting integral equation is handled by the space-time boundary integral equation method. The transient response for the case of a thin wire isolated in free space computed by this direct time-domain approach is compared with results obtained by another method solved using data derived from frequency-domain analysis. Results for various other configurations are also presented.

POSTPROCESSING OF THE HUMAN BODY RESPONSE TO TRANSIENT ELECTROMAGNETIC FIELDS

The post-processing of human exposure to a transient electromagnetic fields is presented in the paper. The mathematical model is based on the cylindrical representation of the human body and the corresponding space-time Hallen integral equation. The Hallen integral equation is solved via the Galerkin-Bubnov scheme of the indirect boundary element method and the equivalent space-time current distribution along the cylindrical body model is obtained. The transient current flowing through the human body is postprocessed in terms of certain measures of quantifying the transient response. These measures arise from circuit theory and they are average and root-mean square value of time-varying current, instantaneous power dissipated in the body and total absorbed energy in the body. Illustrative numerical results are presented.

Root-mean-square measure of nonlinear effects to the transient response of thin wires

A root-mean-square (rms) measure of effect of nonlinear loading on the transient response of thin wires is proposed. The transient behavior of nonlinearly loaded wires is analyzed directly in the time domain. The problem is formulated via the space-time Hallen integral equation. The equation is solved by the space-time Galerkin Bubnov boundary element procedure. Numerical results for the transient response of a thin wire computed by a time domain code based on this method are compared with results obtained from a frequency domain code. Some illustrative numerical results for the spatial distribution of the rms values of time varying currents are also presented.