Galerkin-Bubnov Scheme Of The Indirect Boundary Element Method Research Articles

Direct time domain evaluation of the transient field transmitted into a lossy ground due to GPR antenna radiation

The paper deals with the direct time domain calculation of a transient electric field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into the lossy half-space. The space–time dependent current along the dipole is governed by the Hallen integral equation which is numerically solved by means of the Galerkin–Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Provided that the current distribution along the GPR antenna is determined, one may compute the related electromagnetic field transmitted into the lossy ground by solving the field integral formulas. Some illustrative computational examples related to the transmitted field into the lower half-space are reported in this paper.

Transient Response of Grounding Electrode using the Wire Antenna Theory Approach

The paper deals with an assessment of transient current induced along the vertical grounding electrode applying the thin wire antenna model in the frequency domain. The formulation is based on the homogeneous Pocklington integro-differential equation. The influence of an imperfectly conducting half-space is taken into account via the corresponding reflection coefficient arising from the Modified Image Theory (MIT). The Pocklington equation is solved using numerical and analytical approach respectively. The numerical solution is carried out via the Galerkin-Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). The transient response is obtained by means of the Inverse Fourier Transform (IFFT). Some illustrative computational examples for the transient current induced at the center of a vertical grounding electrode are presented in the paper.

Measurement and modeling of the propagation of the Ripple Control Signal through the distribution network

The paper deals with the estimation of the vertical propagation of the Ripple Control Signal (RCS) through the distribution network segment. Magnitude of the RC signal is determined at various points in the network using in-situ selective pulse measurements as well as simplified model of the distribution network based on the antenna theory. Measurements are carried out in the 3-phase system on 3 voltage levels, 110kV, 10kV and 400/230V, respectively, in either indirect or direct configuration, depending on nominal voltage. Distribution network segment is modeled as an antenna excited with voltage source on one end and terminated with corresponding impedance on the other. The current induced along the distribution cable is determined by solving the corresponding Pocklington integro-differential equation in the frequency domain. The numerical solution is undertaken via Galerkin–Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Results obtained via different methods seem to agree satisfactorily.

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.

Comparison of analytical and boundary element modeling of electromagnetic field coupling to overhead and buried wires

The paper deals with various approaches for the analysis of electromagnetic field coupling to horizontal straight line of finite length in the presence of a lossy half-space based on the theory of thin wire antennas. The formulation is posed in the frequency domain and it is based on the corresponding Pocklington integro-differential equation. Throughout this work the Pocklington equation is solved numerically via the Galerkin–Bubnov scheme of the indirect boundary element method (GB-IBEM) and analytically. The obtained results are compared to NEC results and to the results obtained by applying the transmission line (TL) model, i.e. to the results obtained by solving the corresponding Telegrapher’s equations.

Analytical versus boundary element modelling of horizontal ground electrode

Different approaches to the analysis of horizontal ground electrode, based on the wire antenna theory have been used in this work. The spatial distribution of the induced current along the electrode is obtained by solving the homogeneous Pocklington integro-differential equation. The spatial distribution of the scattered voltage along the electrode is computed using the generalized telegrapher's equation. The assessment of current and voltage induced along the electrode is carried out using both analytical and numerical approaches. The numerical solution of integral expressions arising from the antenna theory model is numerically handled via the Galerkin–Bubnov scheme of the Indirect Boundary Element Method (GB-IBEM). Some illustrative results for the current and voltage induced along the horizontal electrode are given in the paper.

Comparison of wire antenna and modified transmission line approach to the assessment of frequency response of horizontal grounding electrodes

The paper deals with different methods for the assessment of frequency response of a horizontal grounding electrode. The approaches are based on the wire antenna model (AM) and modified transmission line model (MTLM) in the frequency domain. The integro-differential relationships arising from the wire antenna theory are numerically handled via the Galerkin-Bubnov scheme of the indirect boundary element method (GB-IBEM), while the modified transmission line (telegrapher's) equations are treated using the chain matrix method and modal equation to derive per unit length parameters. The per unit length parameters of buried conductors are computed using the modal equation. Some illustrative numerical results are presented in the paper.