The application of the transmission line matrix and the finite-difference time-domain methods for two and three dimensional numerical modelling of ground probing radar (GPR) is the subject of this thesis. Basic principles of GPR are discussed at the outset and the suitability of the chosen approach for its numerical simulation is demonstrated. Efficient absorbing boundary conditions are introduced in the two dimensional formulation of the transmission line matrix in order to limit the computational domain. Their performance is evaluated and it is demonstrated that by using different forms of implementation they can perform similarly or better than the finite-difference time-domain method. Two dimensional models are used to study the effects of the constitutive parameters of the subsurface to the GPR signals and the limits of horizontal and vertical resolution as well as responses from common geological targets. A solution to the instabilities introduced by absorbing boundary conditions in the three dimensional transmission line matrix method using the symmetrical condensed node is reported as a modification of an existing formulation. The good performance of this absorbing boundary condition in free-space scattering problems is demonstrated using a scattering field transmission line matrix model. Three dimensional models based on these numerical techniques are used to study the GPR responses from small localized targets and the advantages and disadvantages of different orientations of the transmitting and receiving antennas. The potential benefit of the use of magnetic field sensors in ground probing radar is demonstrated using the three dimensional finite-difference time-domain model. Comparisons between the two formulations studied for the simulation of ground probing radar are reported.

The investigation of transmission-line matrix and finite-difference time-domain methods for the forward problem of ground probing radar

A state-of-the-art model of time-domain coupling between electromagnetic field and thin wire structures using the transmission-line matrix (TLM) method is presented. The concept of accounting for electromagnetic presence of thin wires by introducing wire networks is described and a general interface between such wire networks and ordinary TLM nodes is derived. A full description of a general wire junction model which can also be used to model straight and bent wire segments is presented. A further generalization of this method to allow for modelling of closely spaced thin wires (or multi-wires) is discussed. Typical results obtained by field simulations of different wire structures are presented to confirm validity of the developed algorithms. Copyright © 1999 John Wiley & Sons, Ltd.

Modelling of coupling between transient electromagnetic field and complex wire structures

Accurate modeling of thin wires in large-scale numerical electromagnetic simulations is very time consuming if fine meshing is adopted. Special treatments of such wires to allow their incorporation into relatively coarse meshes have lead to the development of thin-wire nodes for the transmission-line matrix (TLM) method. Previous models require the use of empirical factors. A novel thin-wire node is presented that is derived from rigorous field theory, requires no empirical factors and is shown to be highly effective. Moreover, virtually no computational overhead is incurred in the use of the new wire node.

An accurate thin-wire model for 3-D TLM simulations

A method for the time-domain simulation of electromagnetic (EM) wave interaction with thin-wires is developed. The technique is based on the standard transmission-line modeling (TLM) technique augmented with systems derived from the telegrapher's equations to represent the propagation of currents in wires. Full details of the numerical algorithms are given and examples are shown to illustrate the application of the technique to typical electromagnetic compatibility (EMC) problems.

Time-domain modeling of electromagnetic wave interaction with thin-wires using TLM

[1] A numerical modeling of Earth's atmosphere is carried out by means of the Transmission Line Matrix (TLM) numerical method with the aim of calculating the Schumann resonance frequencies. The numerical results obtained are very close to the experimental ones and those obtained with the widely accepted two-scale-height ionospheric model, which allows us to affirm that this is a valid numerical tool for predicting the Schumann frequencies in the atmospheres of other planets and moons. The great flexibility of the TLM numerical method also allows the study of slight shifts in the Schumann resonance frequencies due to an increase in electrical conductivity at the Earth's poles, originating from high-energy particle precipitation emitted from the Sun in conjunction with solar flares. A slight increase in the first Schumann resonance frequency is observed during these events, which is associated with a reduction in the dimensions of the electromagnetic cavity.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002JA009779

A numerical simulation of Earth's electromagnetic cavity with the Transmission Line Matrix method: Schumann resonances

In this paper, the dispersion characteristics of a TLM mesh formed by interconnected symmetrical condensed nodes with stubs are calculated using two different formulations. The dispersion relation derived is an implicit function of the wave number, frequency, dielectric permittivity, and magnetic permeability. Group and phase velocities are obtained for the three fundamental directions and different values of the relative permittivity. The study demonstrates that an increase in the modeled-medium permittivity leads to a decrease in the cutoff frequency for TLM numerical results. >

Dispersion analysis for a TLM mesh of symmetrical condensed nodes with stubs

The additional capacitance and inductance introduced by a conducting wire can be modelled in the transmission line modelling (TLM) method by a special node. A symmetrical transmission-line structure is proposed for the modelling of wire junctions in a coarse mesh. The model is tested by calculating the response of a wire-cross scatterer and the RCS of a perfectly conducting plate simulated by means of a square wire mesh. Although, initially, TLM was not developed for solving wire structures, the results are in good agreement with the theoretical and moment-method solutions traditionally used for this type of structure. >

Wire-junction matrix model for the TLM method

This paper presents the analytical expressions of group and phase velocities as a function of frequency in the TLM-symmetrical-condensed node mesh for the three fundamental directions. The direction /spl lsqb/1, 1, 1/spl rsqb/ happens to be more dispersive than the directions /spl lsqb/1, 1, 0/spl rsqb/ and /spl lsqb/1, 0, 0/spl rsqb/, giving the TLM-symmetrical-condensed formulation dispersion characteristics similar to those of the FD-TD algorithm with a Courant number of 1//spl radic/3. >

Group and phase velocities in the TLM-symmetrical-condensed node mesh

A new wire model to simulate the presence of loads in thin wires is presented. The scattering matrix of the node is provided and examples of resistive, reactive, and nonlinear loads are included and compared with a moments-method solution.

G. Gimenez

Papers

Dispersion analysis for a TLM mesh of symmetrical condensed nodes with stubs

Wire-junction matrix model for the TLM method

Group and phase velocities in the TLM-symmetrical-condensed node mesh

Loaded-wire node for TLM method