Galerkin-Bubnov Indirect Boundary Element Method Research Articles

Assessment of Transmitted Power Density in the Planar Multilayer Tissue Model due to Radiation from Dipole Antenna

Recent relevant safety guidelines IEEE-Std C95.1- 2019 and ICNIRP-RF Guidelines 2020 have converged towards 6 GHz as a transition frequency from specific absorption rate (SAR), as basic restriction quantity, to absorbed power density (APD). Namely, the penetration of electromagnetic waves into the human tissue rapidly decreases as frequency increases, therefore, tissue heating can be considered as superficial above 6 GHz. However, besides the APD, an alternative internal dosimetric quantity transmitted power density or TPD is sometimes computed since its relation to SAR is more obvious and is easier to obtain. This paper deals with an analytical/numerical approach to determine TPD in planar multi-layered model of the human tissue exposed to the dipole antenna radiation. Analytical approach deals with assumed sinusoidal current distribution, while numerical approach pertains to the determination of current by solving the corresponding Pocklington integro-differential equation via Galerkin-Bubnov Indirect Boundary Element Method. The novelty presented in this paper with respect to previous work is a multilayer geometry whose effects are considered via the corresponding Fresnel plane wave reflection/transmission approximation. Some illustrative results for current distribution, transmitted field, volume power density (VPD) and TPD at various frequencies and distances of the antenna from the interface are given.

Uncertainty Quantification for the Transient Response of Human Equivalent Antenna Using the Stochastic Collocation Approach

The paper deals with the uncertainty quantification of the transient axial current induced along the human body exposed to electromagnetic pulse radiation. The body is modeled as a straight wire antenna whose length and radius exhibit random nature. The uncertainty is propagated to the output transient current by means of the stochastic collocation method. The stochastic approach is entirely nonintrusive and serves as a wrapper around the deterministic code. The numerical deterministic model is based on the time domain Hallen integral equation solved by means of the Galerkin-Bubnov indirect boundary element method (GB-IBEM). The stochastic moments, i.e., the mean and the variance of the transient current, are calculated. Confidence margins are obtained for the whole duration of the transient response as well as for the maximal current value. The presented approach enables the estimation of the probability for the induced current to exceed the basic restrictions prescribed by regulatory bodies. The sensitivity analysis of the input parameters indicates to which extent the variation of the input parameter set influences the output values which is particularly interesting for the design of the human equivalent antenna.

Integral Equation Formulations and Related Numerical Solution Methods in Some Biomedical Applications of Electromagnetic Fields

The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.

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.

Time-Domain Generalized Telegrapher's Equations for the Electromagnetic Field Coupling to Finite Length Wires Above a Lossy Ground

In this paper, a time-domain variant of the generalized telegrapher's equations for transient electromagnetic field coupling to a finite-length wire above a lossy half-space is derived. The approach is fully based on the thin-wire antenna theory. The lossy ground effects are taken into account by means of the reflection coefficient approximation. The obtained equations are handled numerically via the Galerkin-Bubnov indirect boundary element method. Computational examples are presented for the case of a single-wire line excited by an electromagnetic pulse excitation source. The obtained results for the induced current along the line are compared with those obtained using 1) the method of moments solution of the electric field integral equation implemented in the numerical electromagnetics code (NEC-4), and 2) the transmission line (TL) theory. It is shown that the results obtained by the proposed method are in excellent agreement with those of NEC-4. It is also shown that the TL approximation yields in general results which are in reasonably good agreement with the full-wave results, especially for the early time response and even beyond the limits of the accuracy of the TL theory. The TL theory can, however, give accurate results only for times before the arrival of the first reflection from the TL terminations and it fails to reproduce accurately the dispersion effects occurring after the first reflection.

Transient analysis of grounding systems for wind turbines

The paper deals with transient analysis of grounding systems wind turbines. A typical wind turbine grounding system arrangement based on ring electrode is analyzed. Special attention is focused to the influence of additional vertical and horizontal electrodes, respectively. Influence of grounding wire placed in cable trench on the transient behavior is studied in detail. The mathematical formulation in the frequency domain is based on the thin wire antenna theory and the related set of Pocklington integro-differential equations. The corresponding transient response is obtained by means of the Inverse Fourier Transform (IFT). The set of Pocklington integro-differential equations is solved by the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) featuring the use of isoparametric elements. A number of illustrative computational examples are presented in the paper.

Generalized Form of Telegrapher's Equations for the Electromagnetic Field Coupling to Buried Wires of Finite Length

In this paper, a generalized form of telegrapher's equations for electromagnetic field coupling to buried wires is derived. The presented approach is based on thin-wire antenna theory. The effect of a dissipative half-space is taken into account via the reflection/transmission coefficient approximation. The conductor losses can be taken into account via the surface impedance per unit length. The derived equations are treated numerically via the Galerkin-Bubnov indirect boundary element method. Numerical results are presented for induced current along the wire, and compared with transmission-line (TL) and modified TL (MTL) approximations, respectively, for the case of perfectly conducting electrode buried in a lossy medium. It is shown that the TL and MTL approximations can result in an inaccurate induced current distribution along the conductor at HFs and for shorter electrode lengths, respectively.

Time-domain analysis of multiple straight thin wires in a non-homogeneous medium

Time-domain analysis of the transient current distribution along parallel wires located at different heights above a real ground is presented. The numerical solution is carried out via time-domain variant of the Galerkin–Bubnov indirect boundary element method (GB-IBEM) of solution extended to handle the case of arbitrary array of parallel wires located in a homogenous lossless medium, above a perfectly conducting (PEC) ground, or above a dielectric half-space. The mathematical formulation is based on the set of coupled space-time integral equations of the Hallen type. Some illustrative numerical results being compared to the results obtained via other methods wherever possible are presented.

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.

Transient analysis of coated thin wire antennas in free space via the Galerkin-Bubnov indirect Boundary Element Method

This paper deals with a time domain analysis of dielectric coated wire antennas in free space. The formulation is based on the Hallen integral equation for loaded wires having a dielectric coating. The coating has been taken into account by means of an equivalent magnetic coating load term. The numerical solution has been carried out via the time domain variant of Galerkin-Bubnov indirect Boundary Element Method (GB-IBEM).