Anna Susnjara

An Efficient Deterministic-Stochastic Model of the Human Body Exposed to ELF Electric Field

The paper deals with the deterministic-stochastic model of the human body represented as cylindrical antenna illuminated by a low frequency electric field. Both analytical and numerical (Galerkin-Bubnov scheme of Boundary Element Method) deterministic solutions of the problem are outlined. This contribution introduces the new perspective of the problem: the variability inherent to input parameters, such as the height of the body, the shape of the body, and the conductivity of body tissue, is propagated to the output of interest (induced axial current). The stochastic approach is based on the stochastic collocation (SC) method. Computational examples show the mean trend of both analytically and numerically computed axial current with the confidence margins for different set of input random variables. The results point out the possibility of improving the efficiency in calculation of basic restriction parameter values in electromagnetic dosimetry.

Stochastic Collocation Applications in Computational Electromagnetics

The paper reviews the application of deterministic-stochastic models in some areas of computational electromagnetics. Namely, in certain problems there is an uncertainty in the input data set as some properties of a system are partly or entirely unknown. Thus, a simple stochastic collocation (SC) method is used to determine relevant statistics about given responses. The SC approach also provides the assessment of related confidence intervals in the set of calculated numerical results. The expansion of statistical output in terms of mean and variance over a polynomial basis, via SC method, is shown to be robust and efficient approach providing a satisfactory convergence rate. This review paper provides certain computational examples from the previous work by the authors illustrating successful application of SC technique in the areas of ground penetrating radar (GPR), human exposure to electromagnetic fields, and buried lines and grounding systems.

A Finite Element Versus Analytical Approach to the Solution of the Current Diffusion Equation in Tokamaks

This paper deals with two efficient approaches for solving the current diffusion equation (CDE), which governs current diffusion through the conductive plasma inside a tokamak and compares them to CRONOS tokamak simulation suite, as well. Namely, CDE is solved via the finite-element method (FEM) and an analytical technique, respectively, and the obtained results are subsequently compared with the solution obtained from the state-of-the-art CRONOS suite with finite-difference calculations. The FEM solution is carried out featuring the use of linear and Hermite type shape functions, respectively, while the analytical solution is obtained by applying certain approximations to the CDE. The tradeoff between different approaches has been undertaken. Thus, the results obtained via the FEM approach (with Hermite basis function, in particular) show very good agreement with the CRONOS results, while also providing the stability of the solution. On the other hand, the results obtained via the analytical solution clearly demonstrate a good agreement with the numerical results in the edge region, which makes it very useful for various applications, e.g., for benchmarking purposes.

Advanced analysis of the transient impedance of the horizontal grounding electrode: From statistics to sensitivity indices

The paper deals with a stochastic analysis of influence of randomly distributed values of certain parameters on the value of the transient impedance of the horizontal grounding electrode. Deterministic model for the transient impedance calculation is based on the antenna theory and corresponding Pocklington integro-differential equation in the frequency domain. The Pocklington equation is solved using previously developed analytical technique, thus obtaining scattered voltage at the input terminal of the grounding electrode and, subsequently, transient impedance. Stochastic collocation analysis is applied by taking into account three different random parameters and performing subsequent analysis of their respective impact.

Stochastic-deterministic and sensitivity analysis of the transient field generated by GPR dipole antenna and transmitted into a lossy ground

The paper deals with a stochastic-deterministic modeling and sensitivity analysis of the transient field generated by a ground penetrating radar (GPR) dipole antenna and transmitted into a lossy ground in time domain. Uncertainties are inherent to the environmental and geometrical parameters pertaining to GPR applications. Such settings include dielectric properties of a soil, the terrain inhomogeneity, surface roughness, uncertainty in detected depth of buried object etc. The stochastic modelling is carried out by means of Lagranges stochastic collocation (SC) method while deterministic model is based on the Time Domain Integral Equation (TDIE) approach and related numerical solution via the space-time variant of Galerkin Bubnovs Indirect Boundary Element Method (GB-IBEM). The presented model provides a mean to rank the input parameters from the most to least influential one and to obtain statistical moments for the transient field values. The paper also aims to combine the time domain techniques with the stochastic method to provide a more complete description of GPR antenna generated fields.

Electric field radiated by a dipole antenna above a lossy half space: Comparison of plane wave approximation with the modified image theory approach

The paper deals with the comparison between the two approaches to account for the presence of a two media configuration when calculating the electric field radiated by the dipole antenna. The first approach features the well-known Fresnel reflection/transmission coefficient approximation which, beside the electric properties of two media, considers also the incidence angle at the interface. On the other hand, the Modified Image Theory (MIT) approach uses the approximation of a normal incidence, thus neglecting the refraction of the wave in the lower medium. The MIT approach thus simplifies the formulation thus providing the analytical solution and the derivation of the time domain computation. In this paper the frequency domain formulation is used. It is based on the Pocklingtons integro-differential equation which is solved numerically using the Galerkin Bubnov scheme of Boundary Element Method. The results obtained by both approaches are compared and conclusions are given regarding the limitations and strengths of the MIT approach with respect to the Fresnel coefficients approximation. The comparison undertaken in this work can serve as a benchmark for the analytical solution modeling and time domain modeling.

Time domain and frequency domain integral equation method for the analysis of ground penetrating radar (GPR) antenna

The paper deals with the comparison between the frequency domain and time domain analysis of transient electric field generated by the ground penetrating radar (GPR) dipole antenna and transmitted into the dielectric half-space for GPR antenna. The time domain integral equation (TDIE) approach is based on the Hallen integral equation for half-space problems. The numerical solution is carried out via the space-time scheme of the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM). The frequency domain formulation is based on the Pocklingtons integro-differential equation which is solved by using the frequency domain scheme of the Galerkin Bubnov Indirect Boundary Element Method. The related transient response is obtained by means of the Inverse Fast Fourier Transform (IFFT). The Integral Equation combined with the transmission coefficient arising from modified image theory (MIT) represents the novel method for obtaining the transmitted electric field of a GPR antenna. This paper brings the comparison of the results obtained by different approaches in solving the Integral Equation. The calculated results agree satisfactorily.

Analysis of multiple-folded spherical helical antenna using the Galerkin-Bubnov scheme of the Boundary Element method

This paper deals with the numerical modeling of electrically short antenna designed as multiple-folded spherical helical antenna (SHA). Such antennas have convenient properties which make them suitable for use in systems such as wireless power transfer. The geometry of SHA is rather complex due to its high level curvature. The problem is formulated in terms of the set of Pocklington integro-differential equations for curved wires which is solved via the Galerkin-Bubnov scheme of the Boundary Element method (GB-IBEM). Some computational examples are given in the paper. The obtained numerical results are compared to some of the results obtained from available commercial software. The agreement is found to be satisfactory.